Flagged emails keep returning and won't synchronize between Apple Mail and Gmail

Simply delete the e-mail entirely, then move it from the trash back to a folder (or the inbox). There should be no more flag.

Here's one approach I found that appeared to work:

• For each flagged email that won't sync
  • Mark it as "red" flagged in the Flagged folder (it should show in the Flagged folder even though it doesn't have a flag next to it)
  • A red flag appears next to the message
  • Clear the flag on the message
  • The number of messages in the Flagged box should be reduced by one
  • Fully quit Apple Mail (Cmd-Q)
  • Restart Apple Mail and the flagged message should remain unflagged

Note: you can select all the emails in the "flagged" folder at once and do this en masse.

As user @ohcibi confirmed, you must force quit Apple Mail for this to work.

Followup: I just ran into this issue again and this process didn't solve it. I believe it may be related to the "Important" tag that Gmail adds. I went into Gmail and unmarked the message as being "Important", and then followed this process. That fixed the problem.

@aardvark's approach didn't work for me. However, a slightly modified version of it did work:

1. Flag all emails that are in the Flagged folder but seemingly aren't flagged.
2. Quit Mail using Cmd-Q.
3. Re-open Mail, those emails should still be in the Flagged folder, but will now have the flag.
4. Unflag them and Cmd-Q a second time.
5. On reload, they should be correctly removed from the Flagged folder.

I frequently had this issue, a real working solution is to fully Quit mail (cmd+Q) and opening again while holding alt by clicking once the Mail icon.