What is the Fastest a Character Can Move in One Turn?

It's unclear whether bonuses to "your speed" apply to flying speeds. If they don't, the fastest you can go is:

• Shapechange into a Storm Giant: 50 ft.
• Monk level 15 Unarmored Movement: +25 ft.
• Barbarian level 5 Unarmored Movement: +10 ft.
• Mobile feat: +10 ft.
• Longstrider spell: +10 ft.
• Boots of Speed: Double speed
• Haste spell: Double speed
• Dash action ×3 (Bonus, Action, and Haste Action): Quadruple speed
• Total: (50 + 25 + 10 + 10 + 10) × 2 × 2 × 4 = 1680 ft per round.

If bonuses to your speed do apply to flying speeds then the fastest you can go is:

• Wind Walk: 300ft.
• Longstrider spell: +10 ft.
• Haste spell: Double speed
• Expeditious Retreat: Doesn't boost your speed, but allows you to Dash as a bonus action.
• Dash action ×3 (Bonus, Action, and Haste Action): Quadruple speed
• Total: (300 + 10) × 2 × 4 = 2480 ft per round.

Sadly, Wind Walk doesn't say anything about letting you benefit from your feats and class features. If it did, you could move at:

• Wind Walk: 300 ft.
• Monk level 15 Unarmored Movement: +25 ft.
• Barbarian level 5 Unarmored Movement: +10 ft.
• Mobile feat: +10 ft.
• Longstrider spell: +10 ft.
• Haste spell: Double speed
• Dash action ×3 (Bonus, Action, and Haste Action): Quadruple speed
• Total: (300 + 25 + 10 + 10 + 10) × 2 × 4 = 2840 ft per round.

Solo

Tabaxi Race (Volo's guide) - 30

5 Barbarian for Fast Movement (PHB) - 10

Elk Totem (SCAG)- 15 (while unencumbered)

5 Monk for Unarmored Movement (PHB) - 10

6 Transmuter Wizard for stone (PHB) - 10

Lvl 1 spell: Longstrider (PHB) - 10

Mobility feat (PHB) - 10

Major artifact with speed (DMG) - 10

Boon of speed (DMG) - 30

Total = 135

Tabaxi Feline agility (Volo's guide) - ×2 speed for 1 turn (resets on not moving a turn)

Boots of speed (DMG) - ×2 speed for 10 minutes after bonus action

Lvl 3 spell: Haste - ×2 movement speed

135 × 2 × 2 × 2 = 1080

Lvl 3 spell: Haste: Dash action - +100% movement

2 Rogue for Cunning action: Dash - +100% movement bonus action

2 Fighter for Action Surge: Dash - +100% movement

Standard Dash action - +100% movement

1080 × 5 = 5400ft for 1 turn, or ~614mph

If you have help from a transmuter wizard, cut out the 6 wizard levels and give them to Monk for an extra 10ft base, or 80ft per move for an extra 400ft, or 5800ft in one turn

Alright, this is gonna be a process, but I believe I can have a character traveling at 7920 feet per round (900 mph), given the absolutely ideal circumstances.

Base Speed

We'll be going with Tabaxi (Volo's Guide to Monsters) for the race, which gives us a base speed of 30 feet.

Next, we're going to take 10 levels in Monk, giving us +20 feet from Unarmored Movement, bringing it to 50 feet. Subclass doesn't matter here, but if we take Way of the Ascendent Dragon (Fizban's Treasury of Dragons), this movement speed can also be flight speed.

We'll take 5 levels in Barbarian, giving us +10 feet from Fast Movement, bringing it to 60 feet. We'll go with the Path of the Totem Warrior (Player Handbook), specifically choosing the Elk totem at 3rd level (Sword Coast Adventurer's Guide), increasing our movement speed by an additional +15 feet when raging, bringing the total to 75 feet.

Next up, we'll take 2 levels in Wizard, specifically choosing the Bladesinging subclass, giving us another +10 feet from the Bladesong, which doesn't require concentration, meaning it can be done at the same time as the Barbarian's rage. Along with the Longstrider spell, which adds an additional +10 feet, lasts for an hour, and also is not concentration, this brings our total so far to 95 feet.

Next, we're going to make sure we have the Mobile feat, adding an additional +10 feet to our movement speed, and we're going to attune to two different artifacts that each have the Major Beneficial Property of adding +10 feet to our movement speed. This will bring us to a base movement speed of 125 feet.

We need a friend who happens to be a 6th level Transmutation Wizard (Player Handbook), who then gives us their Transmuter's Stone, increasing our speed by another +10 feet, bringing the total to 135 feet.

Last but not least, we're going to take 2 levels in Fighter and 1 level in Sorcerer, choosing the Wild Magic subclass (Player Handbook), but most importantly for now, that will bring us to level 20, making the Boon of Speed (Chapter 7: Other Rewards, Dungeon Master's Guide) available to us, adding an additional +30 feet, which brings our grand total base movement speed to 165 feet.

Multipliers

First off, we're going to use our third attunement slot to get some Boots of Speed, which allow us to double our movement speed.

Then, we're going to have our Transmutation Wizard friend cast Haste on us, doubling our movement speed again, and giving us an additional action to work with later.

Lastly, we're going to use the Feline Agility trait that the Tabaxi has to double our speed a third time. All of these abilities don't just increase our speed (like the dash actions does), but actually double it, bringing our grand total movement speed to 1320 feet per round.

Dashing

Now comes the fun. With our movement speed of 1320 feet per round, we're going to dash using every available action we have.

We can use our initial action, our bonus action (Step of the Wind), our Hasted action, and an action surge to take one more, thanks to our 2 levels in fighter.

Additionally, we're going to play with probability here and use our level in Wild Magic Sorcerer. If we have a Wild Magic Surge and roll 01-02 on the table, that means we roll on the table at the start of each of our turns for the next minute. If we get extraordinarily lucky, we'll roll 81-82, which requires us to take an additional action immediately. We can use this additional action to add one extra dash onto the pile.

Recap

Race: Tabaxi

Levels:

• 10 Monk (Way of the Ascendent Dragon)

• 5 Barbarian (Path of the Totem Warrior)

• 2 Wizard (Bladesinging)

• 2 Fighter

• 1 Sorcerer (Wild Magic)

Base Speed & Modifiers:

• 30 feet
• +20 (Unarmored Movement, Monk)
• +10 (Fast Movement, Barbarian)
• +15 (Elk Totem, Barbarian)
• +10 (Bladesong, Wizard)
• +10 (Longstrider Spell, Wizard)
• +10 (Mobile feat.)
• +10 (Major Beneficial Property Artifact)
• +10 (Major Beneficial Property Artifact)
• +10 (Transmuter's Stone)
• +30 Boon of Speed

Multipliers:

• Haste Spell x2
• Boots of Speed x2
• Feline Agility x2

Dashes:

• Base Movement Speed
• Action
• Bonus Action (Step of the Wind)
• Hasted Action
• Action Surge
• Wild Magic Action

1320 x 6 = 7920 feet per round or 900 mph

With boons and luck 21,000 feet movement (2,386 mph) [101,120 feet allowing non-DMG items]

First, This answer is built on the shoulders of giants (Storm Giants?). I'd never have come up with all the tricks just by myself. This answer uses another basis than most of the other answers that nearly all have a chassis of Monk 10 / Barbarian 5 for the speed increases those classes provide.

Second, the question limits what you can use:"level 20 with any magic items in the DMG, and any spells", so there is no resctriction on spells, races and classes but this is using:

• no magic items that are not in the DMG (no Eagle Whistle from Hidden Shrine of Tamoachan or Chronolometer from Acquisitions Incorporated) - even if they would make for faster movement
• movement has to happen in one turn, as per the question title, additional movement you could do with Reactions on other turns during the same round doesn't count.

The question does not specify that you must be able to do everything solo with a single character, nor that you must be able to sustain that speed over several rounds after a single round where you achieve it. So like other answers, this one assumes you can have other party members (also of 20th level, like you) help out, which makes it easier to get around restrictions such as spell lists or concentration, and adds more enhancing features than you could pack into the 20 levels of a single character.

Next, Glyph of Warding. Is it possible to cast spells with a range of Self into a Glyph of Warding so they can affect others - for example Ashadalon's Stride, or Shapechange which are Self spells? While I personally think this is up to the DM, the consensus for this is yes, you can, so I will use that for the answer.

Lastly, I am not sure if boons should be part of this, as they are not mentioned and boons go beyond just being level 20, so I will call them out separately. Lack of boons limits upcasting of payload spells into spell glyphs to 8th level, as the 9th level slot is needed for the glyph, and 20th level casters only have one slot of each, meaning that you cannot have someone cast both a 9th level glyph and cast Shapechange or Stride at level 9 into it without boons changing that.

Our character is a small Tabaxi Artificer 14 / Figther 2 / Bladesinger Wizard 2 / Wild Magic Sorcerer 1 / Immortal Mystic 1 (or something else if we don't use Mystic). The artifcier on level 14 gets Magic Item Savant, which he uses to attune a total of 5 magic items:

You can now attune to up to five magic items at once.

(He also owns a set of bracers of celerity for +10 speed, and a pair of wayfarer's boots for +10 speed, but alas he cannot use them, as he already is wearing boots of speed, and needs his attunement slots for his eclectic artifact collection).

Base Speed

• Race: Tabaxi (Mordenkainen Presents: Monsters of the Multiverse), 30ft walking speed, Feline Agility, size Medium or Small (pick Small).
• Spell Shapechange: cast as a wizard from a 9th level spell scroll with a successful spellcasting ability check of DC 19. There are ways to boost this check so that you can ensure automatic success with +18 or better to the roll¹, as a 1 only autofails on Attacks. You Shapechange into a Quickling for a base speed of 120 feet. Shapechange lets you retain features from your race and class, so you still have access to Feline Agility that you need later on.
• 4 artifacts, each with 2 major properties of increased walking speed by +10: +80 walking speed.
• Bladesinger Wizard 2: Spellcasting and Bladesong, +10 walking speed. (Use a bonus action to activate on an earlier turn.)
• Spell Longstrider: +10 speed. (Cast as a wizard in advance.)
• Mobile feat: +10 speed.
• Squat Nimbleness feat (Xanathar's Guide to Everything) can be taken by any Small race. +5 speed.

Support from your team

• 17th level Wizard (any school) to cast Ashardalon's Stride for you into a Glyph of Warding. (If you allow boons, they need to be 20th level to access those). Ashardalon's Stride, cast at 8th level and triggered from a Glyph of Warding to avoid concentration: +45 speed. They create additional glyphs with haste, and expeditious retreat (which will provide extra Dash actions).
• Oath of Glory Paladin Aura of Alacrity (7th level) in which you start your turn: +10 walking speed.
• Transmutation Wizard Transmuter's Stone (6th level): +10 speed.
• Graviturgy Wizard Adjust Density to half weight (2nd level): +10 speed.
• College of Creation Bard Having an Animating Performance (6th level) item affect you with Irrpressible Dance, increase option: +10 speed.

This all gives you a walking speed of 120 (base Quickling), +80 Artifacts, + 45 Ashardalon's Stride, +5 Squat Nimbleness, + 10 Bladesinger +10 Longstrider, +10 Mobile, +10 Aura of Alacrity, +10 Transmuter's Stone, +10 Adjust Density, +10 Irrepresible dance = 320 walking speed

Double-ups

• Spell Haste: x2 speed, extra action for Dash. (Concentration, so from a glyph; alternatively you could drink a potion of speed).
• Boots of Speed: x2 walking speed. (Use a bonus action to activate on a previous turn; this occupies your last attunement slot.)
• Tabaxi Feline Agility x2 speed (one turn only)

Total multiplier x 8

Moves

• Normal Move
• Dash action
• Dash bonus action from Expeditious Retreat
• Dash extra action from Haste
• Dash extra action from Fighter 2 Action Surge
• Reaction move from allied Fighter (Battle Master) trigger Maneuvering Attack: if you witness the attack, you can use your Reaction to move up to half your speed. To make this happen on your turn, the fighter must Ready an action to attack in response to something visible you do.

Total moves 5.5

Total movement = 320 x 8 x 5.5 = 14,080 feet

Boons

I left out Epic Boons in the main answer, as as they represent progress once you already reached 20th level, and I think allowing them might need to be called out. However, the question is rather terse, and if they are allowed, then you can do better:

• Boon of High Magic lets you gain one 9th-level spell slot, provided that you already have one, so your wizard friend with the boon then would have two 9th level slots, and could upcast both the Glyph and Stride, setting up a Glyph for you with a +50 Stride (+5 better), and another one with Shapechange.
• Boon of Speed would give you another +30 walking speed (plus a bonus action Dash, but we do have other ways to get that already).

These additions would get you to a unmultiplied speed of 355.

After multipliers and actions, without resorting to lucky rolls, 15,620 feet of movement.

Less dependable methods that need luck or DM buy-in

I on purpose also left out features that require you to roll lucky to get a speed boost, because I feel these are of a different quality than those that you can reliably pull off, but of course, as this is a theoretical optimization question anyways so it could be possible to be very lucky.

(Obviously, getting any magic items, in particular the artifcacts with speed properties also need luck and/or DM placet, but once you have them, you know what you can do with them. Here, you have to gamble while you actually are trying to pull off the movement).

These would add

• Alchemist Artificer 3 Experimental Elixir, 1/6 chance to get Swiftness, +10 walking speed.
• Immortal Mystic 1 (Unearthed Arcana) Celerity Discipline psychic focus : +10 walking speed.
• Flesh warping by a Sibriex (Kudos to this answer). If you willingly submitted yourself and your DM used the variant rules for Flesh Warping, you could permanently be transformed with incredibly long and springy legs as a result of [56-60] on the Flesh Warping table. However, I don't think this permanent transformation is an ongoing spell effect, and so it likely would not carry over to your Shapechanged form. But: you could have a Sibiriex squeezed away into a demiplane, have your wizard open the demiplane and get him to flesh warp your quickling form right when the action happens. You would have to be failing your save (which again you cannot do willingly), the DM would have to use the alternate rules, and you would have to roll a 56-60 (a 1 in 20 chance). All of it very unlikely, dangerous, and hard to control, but theoretically possible. +10 walking speed.

New speed 355 + 3 x 10 = speed 385

• Your Bard standing behind you and taking a Ready action the prior round to cast dissonant whispers on you once you start to move. The spells says: "The target must make a Wisdom saving throw. On a failed save, it takes 3d6 psychic damage and must immediately use its reaction, if available, to move as far as its speed allows away from you". You cannot fail a save voluntarily in 5e 2014, so there is a risk to not fail this save, but you can use tricks like the Lucky feat or a Divniation Wizard friend with a low-rolled Portent to help out. In any case, if you are affected, this will upgrade using your Reaction from 1/2 move to a full move, for a total x6 moves.
• Wild Magic Sorcerer 1: Wild Magic Surge. You first need to cast a leveled spell, and get a lucky 01-02 (1/50th chance) with your DMs buy-in to roll in one of the rounds before the speed-run round. This will allow you to roll in any of the following rounds again. Then rolling a 81-82 (1/50 chance) will get you an additional action. With a chance of 1 in 2500 you get an extra action, for a total of x7 moves.

Total moves 7.

New overall movement 21,560 feet

If you could use magic items from other sources

• A Chronolometer, a very rare item, would replace one of the artifacts, slowing your unmultiplied speed by 20 feet, but giving you on a roll of 1-3 on d6 (1 in 2 chance) an additional action on your turn and doubling your speed until the end of the turn. (It also can give you an extra move as a reaction, but we have that covered already).

• The Infernal Machine of Lum the Mad, itself an artifact, could replace the other artifact. It has 1d4+1 random beneficial properties. If you roll a 48 on the table of 100 possible options you get +10 walking speed. Roll it all 5 times in a row (a chance of 1 in 4*100^5 or 40,000,000,000), it will give you +50 walking speed, instead of +20. (It also has one option that sets your speed to a flying speed of 150, but you lose all other movement - and we want a lot of other movement).

Together these two would increase your unmultiplied speed by 10 vs two "generic" artifacts, to 395 feet. They would double the speed once more to x 16, add one more move to 8 moves for 395 x 16 x 8 = 50,560 feet.

• You then can double that by flying at twice your walking speed with the Eagle Whistle (no attunement needed), for 101,120 feet in one turn.

But I think, according to the parameters of the question, all this is not allowed.

---

¹ There are multiple ways to boost an ability check. For example you can have Int 30 for +10 ability modifier from perusing multiple copies of a Tome of Clear Thought, a cleric can give you guidance for +1d4, as a peace cleric they can can forge an Emboldening Bond with you for another +1d4, a bard can give you bardic inpiration for up to +1d12, an artificer can give you up to +10 (if they also read a lot of Tome of Clear Thought) as a reaction to you making the check, etc.

P.S. Since many of these features need less than 20 levels, you can combine them into fewer actual 20th level characters, for example your group could look like this

• a Bladesinger Wizard 2 / Artificer 14 / Fighter 2 / Wild Magic Sorcerer 1 / Mystic 1 to run around
• one Transmutation Wizard 20 (Glyph, Stride, Shapechange)
• one Oath of Glory Paladin 7 / College of Creation Bard 6 / Graviturgy Wizard 2 / Peace Cleric 1 (for helping with the spell scroll¹) / Battlemaster Fighter 3 / anything 1
• one Alchemist Artificer 7 / anything 13 (Flash of Genius, Experimental Elixir)

P.S.S. Solo Speed

Being a Small Tabaxi level 18 wizard (bladesinger or transmuter) / level 2 Fighter, without help from others, you can cast Ashardalon's Stride at level 8 into a glyph, Expeditious Retreat into another glyph, and use Shapechange with concentration as your level 9 spell to get:

Walking speed of 120 (Quickling) + 10 Bladesinger + 45 Ashardalon's Stride, +10 Longstrider, +10 Mobile, +5 Squat Nimbleness, +40 Artifacts = 240 walking speed

Haste (from yet another prepared glyph or Potion of Speed) x2, Boots of Speed x2, Feline Agility x2 (for one turn), total multiplier x 8

Normal Move 1, normal action Dash 2, Expeditious Retreat bonus action Dash 3, Haste extra action Dash 4, Action Surge action Dash 5 = 5 total moves.

240 x 8 x 5 = 9,600 total movement in one turn.

This is better than being a level 20 wizard having access to a higher speed with Boon of High Magic and Boon of Speed, which togehter would add 35 speed, but in exchange for those you now lack Action surge and lose a move. (275 x 8 x 4 = 8,800 total movement)

Tabaxi (from Volo's Guide to Monsters)
Monk 18 / fighter 2

60ft
+10 ft longstrider +10 ft transmuter stone +10 ft mobile

90 ×2 tabaxi
180 ×2 haste
360 ×2 boots of speed
=720ft

720 Move
1440 Action
2160 Bonus action
2880 Haste action
3600 Action surge

That's a total of 3600 ft in 1 round.

Okay, I think I have calculated the fastest a character can move in ideal conditions without teleporting. Bear with me, as it's pretty contrived. I am interpreting increases to "speed" to apply to all speeds, whereas I am interpreting increases to "walking speed" to only apply to walking speed, so we need to find the fastest walking speed we can.

Edit: as @David Coffron mentioned, it works to use Shapechange instead of Wild Shape: you still keep your class and racial features, and this character is capable of casting it from a Level 9 Spell Scroll with their Wizard levels (and with an Intelligence ability check of 19, but let's assume we make that). Shapechange is concentration, and is Target: self, so if we want Haste too we will need to have it cast on this character or use a Potion of Speed. As such we can remove the Druid levels and take more Monk, boosting the character's speed even higher.

Base Speed

• Race: Tabaxi, base 30ft walking speed, Feline Agility feature.
• Barbarian (Totem Warrior: Elk) 5: +10 speed from Fast Movement, +15 walking speed from Totem Spirit: Elk. (Needs to be raging for Elk Totem Spirit: do this as a bonus action on an earlier round, and make sure you keep your rage going until you can pull this turn off.)
• Fighter 2: Action Surge.
• Monk 10: +20 speed from Unarmored Movement.
• Sorcerer (Wild Magic) 1: Wild Magic Surge. (This helps us, but requires casting a leveled spell and getting very lucky! See below in the Setup section.)
• Wizard (Bladesinging) 2: Spellcasting (for the spell scroll) and Bladesong, +10 walking speed. (Use a bonus action to activate on an earlier turn.)
• This takes us to Level 20 to get Epic Boons.
• Mobile feat: +10 speed.
• Boon of Speed: +30 walking speed, bonus action dash once per short rest.
• Shapechange spell active: Shapechange into a quickling with base 120ft walking speed. Cast Shapechange with a Level 9 spell scroll using your 2 levels in Wizard, make the DC 19 Intelligence ability check, and make sure you maintain concentration.
• Longstrider spell active: +10 speed. (Not concentration; cast it on yourself with your Wizard levels or have your friendly Wizard cast it on you.)
• Artifact 1 (1st attuned) with two major properties of speed: +20 walking speed.
• Artifact 2 (2nd attuned) with two major properties of speed: +20 walking speed.
• An ally Artificer (Alchemist) with the Level 3 feature Experimental Elixir and a bit of luck gets you Swiftness, +10 walking speed.
• 2x ally Fighter (Battle Master) at level 3 for maneuvers, or anyone with the Martial Adept feat who has access to Maneuvering Attack: A friendly creature who can see or hear you can use its reaction to move up to half its speed. Having two is very important to allow us to use a reaction before our turn and a reaction after our turn, getting us two in one round.
• An ally Paladin (Oath of Glory) with the Level 7 feature Aura of Alacrity: +10 walking speed.
• An ally Wizard (Transmutation) with the level 6 feature Transmuter's Stone: +10 speed.
• Haste spell active: x2 speed, hasted action Dash. (Concentration, and 3rd level; have your friendly Wizard cast it on you.)
• Boots of Speed (3rd attunement): x2 walking speed. (Use a bonus action to activate this on a previous turn.)

All up, this gives us a base walking speed for the round of [120 (quickling) + 10 (Barbarian Fast Movement) + 15 (Totem Spirit Elk) + 20 (Monk 10 Unarmored Movement) + 10 (Bladesong) + 10 (Mobile) + 30 (Boon of Speed) + 10 (Longstrider) + 20 (Artifact 1) + 20 (Artifact 2) + 10 (Experimental Elixir) + 10 (Aura of Alacrity) + 10 (Transmuter's Stone)] x 2 (Haste) x 2 (Boots of Speed) = 1180ft.

Setup

As mentioned, on previous rounds we want to have used our action to cast Shapechange into a quickling, a bonus action to rage to activate Elk Totem Spirit, an action or bonus action to cast a leveled Sorcerer spell to activate Wild Magic Surge, a bonus action to trigger Bladesong, and a bonus action to trigger the Boots of Speed's doubling effect. We also need to have Longstrider and Haste active and be within 5ft of the ally Paladin with Aura of Alacrity. For the Wild Magic Surge (thanks @oneroi13 for spelling this out in this other answer!) we need the DM to cooperate, having us roll after casting the leveled spell, then either roll a 1 on a d20 to trigger a Wild Magic Surge or trigger it automatically with Tides of Chaos, then get a 01-02 on 1d100 on the Wild Magic Surge Table to trigger "Roll on this table at the start of each of your turns for the next minute, ignoring this result on subsequent rolls."

The Round

Then, we need the round to progress like this:

• Our ally Battle Master Fighter or whoever has Maneuvering Strike moves before us in initiative, hits a creature with a weapon attack, and triggers Maneuvering Strike from a place we can see or hear them, allowing us to use our reaction to move up to half our speed (590ft).
• At the start of the turn we pull this off roll 81-82 on 1d100 on the Wild Magic Surge Table to trigger "You can take one additional action immediately."
• Then we activate the Tabaxi feature Feline Agility: "Your reflexes and agility allow you to move with a burst of speed. When you move on your turn in combat, you can double your speed until the end of the turn. Once you use this trait, you can't use it again until you move 0 feet on one of your turns." This doubles our speed again to 2360ft.
• Then we Move, use our action to Dash, use our bonus action to Dash (from the Boon of Speed – or using a Ki point to use the Monk's Step of the Wind, which we also have), use our hasted action to Dash, use Action Surge and use that action to Dash, and use our extra action from Wild Magic Surge to Dash. That's 6 moves at 2360ft each, so 2360*6 = 14160ft.
• We end our turn within sight or hearing range of our second ally Battle Master Fighter, who luckily moves after us in initiative. We have our reaction back, so on their turn they hit a creature with a weapon attack, and trigger Maneuvering Strike from a place we can see or hear them, allowing us to use our reaction again to move up to half our speed. Unfortunately Feline Agility wore off at the end of our turn, so that's only another 590 ft.

In total that round, that's 14160 + 590*2 = 15340ft over 6 seconds, or 1400 miles per hour – just over Mach 2.3. So you can expect sonic booms as you move! Admittedly, the question was only about how fast you can move on your turn, so that's just 14160ft over 6 seconds, which is only slightly slower, and you can forgo the complex positioning with the two Battle Masters.

---

Caveats

I looked into making this work with Wind Walk, as the base 300ft move would be incredibly useful. Unfortunately, it is too hard to boost without any of the features that increase walking speed. I did manage to get it up to 7920ft per round, and you can still do the Battle Master cheese, but unfortunately the Boots of Speed only apply to walking speed, and without that doubling it is not quite enough to match what I've laid out above.

@Ibenadar mentioned the 303 Monk in this other answer which can supposedly move at 16800ft per round while Wind Walking, and looking into it, it seems to assume that all increases to speed or walking speed stack on top of Wind Walk's base speed. I don't think that's reasonable, at the very least given how Wind Walk specifies flying speed while e.g. the Boon of Speed explicitly only boosts walking speed, so while it's a bit faster than what I've given, I don't think it's actually attainable.

Admittedly, a lot of this is subject to the DM. As mentioned right at the beginning, I am using a specific interpretation where features that add to "speed" add to all base speeds (walking, flying, climbing, swimming, burrowing etc), whereas features that add to "walking speed" only add to the walking speed. Whether bonuses to "speed" are only meant to apply to walking speed is contentious and unclear, but I am going with the Crawford clarification that bonuses to speed apply to all speeds. Further discussion here.

It also depends on the DM allowing rolling for a Wild Magic Surge, which should be pretty reasonable but isn't a guarantee (and then the incredible luck getting the right Wild Magic Surge afterwards, though that isn't DM-dependent). More pressingly, it also depends on attuning to two artifacts both of which have 2 major beneficial properties to speed. Artifacts are only meant to be made by the gods so it's entirely up to the DM whether the required artifacts exist at all. After this, it's also unclear whether a single major beneficial property of speed is a unique magical effect and whether they stack – if the DM rules that they don't that reduces our artifact speed bonus by 30ft.

Lastly, we are getting a lot of mileage (lol) from the Tabaxi's Feline Agility racial feature. It is very questionable whether that still works when Wild Shaped or Shapechanged: you keep class and racial features, but only if the new form is physically capable of doing so. Unfortunately, Feline Agility has the barest minimum of fluff: "Your reflexes and agility allow you to move with a burst of speed." So it's unclear if it should work only on creatures that are sufficiently similar to Tabaxi (as it's a Tabaxi racial feature), creatures that are sufficiently feline (from the name Feline Agility) or any creatures that are sufficiently agile. This ruling is also very dependent on the DM, and losing that doubling will reduce the maximum speed quite significantly, so it's important to consider that if anyone is bold enough to try this in an actual game.

Result

Assuming all my assumptions hold, based on the above calculations the quickest a character can travel without teleporting in a single round is 15340ft, or 14160ft just on their turn. With a lot of luck for the Wild Magic shenanigans, Experimental Elixir of Swiftness and ally positioning, but it still gets you there!

This post is fairly old by now, and while the OP's body text limits to magic items in the DMG, I wanted to add the Intercontinental Ballistic Tabaxi from Reddit in the spirit of the title question because it increases the max speed quite significantly.

We will be flying 75,040 feet this turn.

Additional note is we will need two friends to help with this, a level 17/3 Transmutation Wizard/Alchemist Artificer with the Boon of Spell Recall and the Metamagic Adept feat with Extended Spell. As well as a level 7/6/2 Oath of Glory Paladin/Creation Bard/Garviurgist Wizard

Your Transmuter will need Shapechange and Glyph of Warding prepared.

As one might guess from the name, we'll be taking a Tabaxi to this speed.

Our classes are as follows:

• 5 levels of Elk Totem Barbarian for +10 from Fast Movement
• 10 in monk for +20 from Unarmored Movement
• 2 Bladesinger Wizard for +10 feet while bladesinging
• 2 levels of fighter of the obligatory Action Surge
• 1 any

With these classes, we're at a base of 70 feet. Now let's add more bonuses. Your transmuter will need to cast Glyph of Warding at 9th level and use Boon of Spell Recall to cast an Extended Spell Shapechange into it. You will then activate the glyph to become a Quickling. This will replace your base 30 foot move speed from Tabaxi with Quickling's 120 foot speed for a net gain of +90.

Thanks to Glyph of Warding, we do not have to maintain concentration of Shapechange and thus can retain its benefits while raging for +15 from Elk Totem.

Next attune to The Infernal Machine of Lum the Mad. This magic item has 5 random effects that you roll for, and rolling a [48] five times can grant up to a +50 bonus to walking speed.

Take the Mobile feat for +10.

Receive a Transmuter Stone with the speed buff from your transmuter friend for +10

Epic Boon of Speed grants another +30.

Voluntarily have a Sibriex warp you using the Flesh Warping variant rule. Since Shapechange was cast with the Extended Metamagic, this means it will still be active when the Warping finishes with slightly under an hour left. A result of [56-60] on the Flesh Warping table grants a +10 to walk speed.

Cast or have Longstrider cast on you for +10.

The Paladin should use their Graviurgist multiclass’ Adjust Density on you, for yet another +10

Have your Transmuter use their Alchemist Experimental Elixir feature to give you a Swiftness Elixir for +10 feet.

Start your turn within range of the Paladin’s Aura Of Alacrity for another +10.

Also start your turn within 10ft of a Dancing Item created by the Paladin's Animating Performance for +10 feet.

Checking in now that the addition is done, we get 70 + 265 = 335 feet of walk speed.

Now, onto the multipliers!

Attune to a pair of Boots of Speed for x2

Have Haste cast on you by your friendly Transmuter, or drink a Potion of Speed for another x2

Shapechange lets you use your original race features if you have proper anatomy so Feline Agility for x2

Use your last attunement slot for the Chronolometer. Once a day, you can roll a d6 at the start of your turn. On a 1-3, your speed is doubled and you gain an extra action. x2

Because multipliers stack, 2x2x2x2 = x16 so 335 x16 is 5,360 feet. This is pretty good, but we're not even close to my stated goal of 75k feet.

Now, the turn.

Have your Paladin use their Bard multiclass to use a readied Dissonant Whispers set to trigger once you start to move (remaining in range for the spell to target you) using Feline Agility: Reaction Move x1

Base movement x2

Action Dash x3

Hasted Dash x4

Action Surge Dash x5

Chronolometer Dash x6

Step of the Wind Dash x7

5360 x 7 is a total of 37,520 feet in a round. But what gives? We're only halfway there. The Hidden Shrine of Tamoachan (in Tales From the Yawning Portal) contains an item called the Eagle Whistle. When you blow it continually, you can fly at a rate of twice your movement speed. There’s no stated action to blow the whistle, only a limit of how long you can use it continuously and has a minimum of one round.

This gives us a final total of 37,520 x 2 for 75,040 feet in one turn. Flying. With no teleportation. This is approximately Mach 11.11.

Wood Elf: 35ft Base walking speed

Monk 12 / Fighter 2 / Barbarian 6

Bonuses

Monk 12: Unarmored Speed +20

Barbarian 6: Fast Movement +10 and with Eagle Totems, you can Dash as a bonus action without using Ki and enemies have disadvantage on opportunity attacks

Fighter 2: Action Surge

Transmuter's Stone: +10

Mobile Feat: +10

Longstrider: +10

Haste: Double Speed

Boots of Speed: Double Speed

Results

Speed = (35 + 20 + 10 + 10 + 10 + 10) × 2 × 2

Movement Speed with buffs: 380ft

Move 5 times on your turn (Dash, Dash with Bonus Action, Dash with Haste Action, Dash using Action Surge, Movement Action)

That's 1900ft per round, or about 215 mph.

I rest my case.

The fastest single round movement speed is one of 3 answers. The fastest is the 303-Monk which has to be lightly beaten until launch.

Using a friendly Transmuter plus magic item property rules - 16,800 feet flying, but all you can do is move and it also requires a friendly Transmuter to flog until ready to maintain Rage whilst the Abjurer Ward covers the HP damage. The 303-Monk covers 3.03miles at Mach 2.37 and is quite angry when it arrives.

Using a friendly Transmuter and only the printed magic items - 16,000 flying

Just by themselves means losing Elk Rage and dropping Monk FM to +10 - 15,400 flying or 14,800 if we forego the Magic Item qualities too

Just by themselves and no Wind Walk has a different build utilizing Druid Wild Shaping and Potion of Speed. This gets - Land 6,800, Swimming 6,800, Climbing 6,000, Burrowing 5,000, Potion of Flying 6,800

Same Druid, but no +5 or +10 speed magic items - 6,200/6,200/5,400/4,400/6,200

Fastest Speed Build - Solo and no Wind Walk
Tabaxi - Wizard 7, Barbarian 5, Druid 4, Fighter 2, Rogue 2
Race - Double speed
Feats - Mobile +10
Class - Barbarian Elk Rage +15, Barbarian Fast Movement +10, Fighter Action Surge +Dash, Cunning Action +Dash
Spells - Longstrider +10, Potion of Speed +Dash & Double Speed, Wind Walk 300ft speed
Objects - Boots of Speed Double Speed, +5 Minor Magic Item Quality, +10 Major Magic Item Quality, +10 Transmuter, Potion of Flying
Boon - Speed +30

Base Movement: 170 feet
60 +10+15+10+10+10+5+10+10+30

Speed Multipliers: 1,360 feet
Boots x2
Haste x2
Tabaxi x2

Number of Moves: 5 x 1,360 = 6,800
Move = 1
Action +1
Bonus (ER or CA) +1
Haste Extra Action +1
Action Surge +1

Fastest Speed Build - Wind Walk + Friendly Transmuter
Tabaxi - Rogue 2, Fighter 2, Elk-Barbarian 5, Monk 11
Race - Double speed
Feats - Mobile +10
Class - Barbarian Elk Rage +15 [walking only], Barbarian Fast Movement +10, Fighter Action Surge +Dash, Monk Unarmored Movement +20
Spells - Cunning Action +Dash, Longstrider +10, Haste +Dash & Double Speed, Wind Walk 300ft speed [unlcear: "While in this cloud form, a creature has a flying speed of 300 feet" - that wording implies that your fly speed DECREASES to 300 if its more than that.] Objects - Boots of Speed Double Speed [walking only], +5 Minor Magic Item Quality[if you make your own], +10 Major Magic Item Quality [if you make your own], +10 Transmuter
Boon - Speed +30

Base Movement: 420 feet
300 +10+15+10+20+10+5+10+10+30 (Mobile+Elk Rage+Longstrider+Unarmored Monk+Major Magic+Minor Magic+Barbarian Fast Movement+Transmuter Stone+Epic Boon)

Speed Multipliers: 3,360 feet
Boots x2
Haste x2
Tabaxi x2

Number of Moves: 5 x 3,360 = 16,800
Move = 1
Action +1
Bonus (CA) +1
Haste Extra Action +1
Action Surge +1

Wood Elf: 35ft speed

Monk level 15 Unarmored Movement: +25 ft.

Barbarian level 5 Unarmored Movement: +10 ft.

Mobile feat: +10 ft

Longstrider spell: +10 ft

Boots of Speed: Double speed

Haste Spell: Double speed

Dash Action x3 (Bonus, Action, and Haste Action): Quadruple speed

Total: (35+25+10+10+10) × 2 × 2 × 4 = 1440 feet per round

Found the ultimate build for speed:

Race: Tabaxi Barbarian: Path of the Totem Warrior 5 Monk: Drunken 10th Ranger: Gloom Stalker: 3rd Wizard: Bladesinging: 2nd

Feat: Mobile

Magic Item: Elixer of Swiftness Magic Item: Boots of speed

Spell: Haste

Start turn within Paladin Aura of Alacrity

Epic Boon of Speed

1 Round: 1 Mile!! Yep that is 5280 feet in 1 round however unlikely