First you have to enable Object Color, that is found in the Properties window, Material tab, then under the Options region Object Color.
One quirk I found, be sure that the diffuse color of the material is pure white [1, 1, 1]. If it is not you will only be able to control the color up to that level. Example: say the material's color is red [1, 0, 0], now because the green and blue channels are 0 you will never be able to get any value in those channels.
Now the material will use the object's color, that color is found under Properties > Object > Display > Object Color*.
To change the object color while the game is running use this bit of python.
cont = bge.logic.getCurrentController() obj = cont.owner # set the game object's color obj.color = [ 0.0, 0.0, 0.0, 1.0] The color method is looking for a vector in the form of [Red, Green, Blue, Alpha], (You can just leave the alpha set to 1, I have yet to find a place where it is used.)
The game UI for changing the color##color
Creating the interface is the most complicated part.
Here is a working demo file with three sliders, one each for red green and blue. The three sliders all have a game property one for each color channel. They also have these logic bricks. The only difference among the three is the property name. 
This script is what takes the input from the logic bricks above, and changes the three values.
scene = bge.logic.getCurrentScene() cont = bge.logic.getCurrentController() own = cont.owner if cont.sensors['Mouse'].getButtonStatus(bge.events.LEFTMOUSE) == bge.logic.KX_INPUT_ACTIVE: posZ = cont.sensors['Mouse1'].hitPosition[2] if posZ > 1.0: posZ = 1 elif posZ < 0: posZ = 0 own.worldPosition.z = posZ prop = cont.actuators["prop"] prop.value = str(own.worldPosition.z) cont.activate(prop) Then another script on the object you want to change the color is this script. A always sensor set to True pulse mode makes the script run constantly.
scene = bge.logic.getCurrentScene() cont = bge.logic.getCurrentController() own = cont.owner r = scene.objects['handle']['r'] g = scene.objects['handle.g']['g'] b = scene.objects['handle.b']['b'] own.color = [ r, g, b, 1.0] 
