The concept of "normal user", "room owner" and "moderator" needs to be expanded into more granular abilities: (imagine file system per-user rights, it's a very similar concept)
- Room owners who can change other room owners' and users' abilities (so you can have some users with limited extra abilities and who can't change other users' abilities)
- Delete own message older than 2 minutes (up to 48 hours/older) — (automatically granted if you have > 10k rep site-wide, like being able to see chat flags, but may be explicitly allowed by a room owner)
- Delete any user's recent message in the room (up to 48 hours of age) — there's a case to be made about not so frequently visited rooms, but we'd have to collect more data from such rooms' regulars to figure out their needs
- Delete any user's message in the room
Deleting messages should be possible in ranges, same as with moving them.
Flags should only propagate outside the room or site after 3-5 minutes if no action is taken by users and if there are no online moderators who can see it in mentions and come into the room to figure it out.