Touching up the coloring on my American, nylon flag. What is the best way to do this? Thank you.
Perhaps try fabric paint available at a serious art supply store. In Australia, I'd would by these, as they set permanently.
Matching your colours will be difficult, so experiment on a scrap of paper, fabric or even a paper plate first. (My experience with plastic paints is that they dry darker.)
Another option is fabric markers, although heat setting the ink with an iron would need to be done carefully and on a low heat setting for nylon. Again, test your technique on a scrap of nylon first.