While handling flags over the past few days, I've noticed something odd. It seems that when closing a question from the queue using the queue's "Close Question" button, the flag is not marked as handled.
I have noticed this in a couple circumstances. First, by questions I have put on-hold myself; when reloading the queue, or refreshing the question's page, I still see the flags there. Also, I have seen flags requesting closing, and seen that another mod has viewed and closed the question, yet the flag remains.
The only other automatic-handling situation was for deleting posts; this seems still to mark the flag(s) as handled as before; it seems only to be Closing which has this trouble.
Per the comments and further information, it seems this only applies when the post has had a Custom flag on it. That makes sense, and I'll be testing it (for example, on one with only a close flag).
In the meantime, I'll note that if intended, the UI could use some improvement there, as the way is works now once we close the question, it's not apparent that the flag(s) are still present.
Just confirmed with a Low Quality flag that when closing from the Mod Queue, the flag is indeed cleared.