3 prong toggle switch help

depends on the switches you want to use, anything is possible

Would you want the switches lit when the LED's are on or off or lit all the time?

What are the current requirements for the LED's different colors?

Also what is the voltage of the LED's?

 

Use these in the "A" configuration, connecting one pole from the blue negative and green negative connections (respectively) to ground, and have a 12V supply going through the other pole when connected have it go through the 2 LED's on each switch

NOTE: Dont order from the link I posted directly, order from the manufacturer, using a different configuration than is listed on Mouser

just wire it like this:

 

That image is for one color, you take one of the negative legs to the switch, you apply the voltage to the LED's separately, and you are turning on and off the ground (negative)

You would need 3 setups like this, one for each color, those switches are configurable to have almost any color LED, and a whole variety of different designs for the switches