When I take my stuff anywhere I make a box out of foam board/gator board for each kit and then line it with mattress foam that I can cut to fit the model. That way I can keep the foam away from the fragile bits and support the kit in the strongest areas. Then put the individual boxes in your bag. Keep in mind when packing that even if you're the only one carrying them they still may get turned upside down so it's best that they are supported from every angle. Hope for the best but prepare for the worst.
Carry-on rules and sizes have changed a lot lately. Make sure the bag will fit or they WILL chuck it under the plane or worse, another plane.
I was going to say "bring some glue for repairs" but air security being what it is...