I wouldn't limit my thinking just to flags. Both countries have symbols too such as a dragon (China) and eagle (US). Isn't what you're really trying to convey is the blending of the two cultures? Your design possibilities could be boundless if you expand beyond flags. Have you considered Asian fabric for part of your design?
My daughter-in-law in Chineese and she and her father did some wonderful painting on fabric for an exhibit of Chineese language symbols and their translated meanings. While it wasn't quilting but rather silk scarves the concept is similar.