The patches show respect to the countries:
A) That the art originated in-Korea.
B) The Country you are learning in, not nesesarily your country, I would see if you can find a patch with the Polish and U.S.A. flag crossed like here:
This one looks good
http://www.polartcenter.com/Polish_and_American_Crossed_Flag_Patch_p/9290090.htm
Thank you for your response. I will try to follow your suggestion. For me it would be a perfect solution, but as you said, I will ask my instructor first.