Hi campchocolate,
Thanks for reaching out to Apple Support Communities. It sounds like you're having an issue with changes to an email flag staying the color you've selected. We're happy to help.
Do you notice this issue occurs when changing the flag color in a specific account, or any?
You also mentioned this only occurs on your iPhone. If the flag color is changed from your Mac or another device does it show as expected on your iPhone? If so, is this again for a specific account, or any?
We ask as the ability to change the flags color may be limited by your email provider. However, we recommend ensuring the steps are attempted to help isolate the issue.
If needed, check out the section "Flag your email" in the article here: Use mailboxes to organize email on your iPhone, iPad, or iPod touch
You can also view helpful information here: Flag and filter emails on iPhone
Cheers!