Flagged mail not showing up

Given that it works in Apple Mail indicates that it's a MailMate issue.

Try enabling the “Raw Flags” column in the message list. Look out
for \Flagged which is the likely value used for this.

If it doesn't show up then try using “Message ▸ Reset...” on a
single pinned/flagged message. Does that help it update?

There were no messages under Raw Flags that displayed \Flagged. Resetting did not change this. What should I try next?

Sorry about the late reply.

That's very strange. We can try generating some logs like this:

• Open the Activity Viewer (⌥⌘0).
• Reset the message again to make it re-arrive.
• Wait for it to arrive.
• Use “Help ▸ Send Server Logs”.

Then I can see if the server reports it having a flag.