GFCI receptacle and 3-way switches
If the kitchen light(s) are tripping the GFCI then there is a problem in one of the lights. They should work just fine on GFCI whether connected to 3-ways or not. 

Do not ignore the problem.

Track it down and repair it. The reason GFCI's or circuit breakers trip is because something is broke (technical term). This is your first sign of a problem. Ignore it at your own, and your family's, peril. The next sign could be someone hurt or a fire.

Good luck!