Not really. Once the paint dried onto the silk flags it stayed very vibrant. If it had too much acid in the paint, over time, it would eat through the silk.
The only Union Civil War flags that I have seen that had paint problems were some done by Louisville flag maker Hugh Wilkins and that came from him rolling the flags up before the paint had dried completely. A couple Union Kentucky colonels were not too happy with those flags.
Still, flags were provided with oil cloth covers to protect them when furled.