I have noticed that a few of my flags (3 out of the last 5) for closure get declined, despite the flagged question later being closed for the very reason specified in my flag. Is there something I am doing wrong or something I am misunderstanding about the flagging system on this site? I do not want to be banned from flagging by the system if too many of my recent flags get declined.
I just dug through the system and found the reasons for the declined flags.
So to understand this we need a short primer on the way close-votes and the flags work.
First, for close-votes there's a review queue, which shows users on question with a pending community close-vote or a pending close-flag at a time, the user may then vote to close that question, skip it or vote to leave it open. If 3 users or 1 mod vote to leave open, the question is removed from the queue with the result "not closed" and if 5 users or 1 mod decide "close" then the question is closed.
Now the status of the flag is automatically decided based on the review queue entry it spawned. If said entry ends with "closed" then the flag is marked "helpful" and if it ends with "not closed / leave open" then the flag is declined.
This also means that if a flag spawns an entry that gets voted to "leave open" and it gets closed afterwards anyways (either by a mod action or by 5 users) you are seeing a declined flag which should have been a "helpful" flag.
And this is exactly what happened in the second declined flag, as can bee seen by this review queue entry review (?) where my co-mod e-sushi decided at 22:59 that the question is not close-worthy but then 15 minutes later closed it anyways.
As for the first declined flag, it was "just" a "boring" case of 1 mod "leave open", again by e-sushi and the question is still open.
As for the third declined flag, again e-sushi decided it should stay open and then it got deleted (but not closed!) subsequently by the owner, which also means that you need at least 10k reputation here on Crypto.SE to see the question body in this review...
If you want to browse the history of queue decisions yourself, you can see it here (in the UI you need to open the queue first and then click "history" in the tabs that appear, it's kinda hidden).
I do not want to be banned from flagging by the system if too many of my recent flags get declined.
From what I saw when looking at your declined flags there is an entry "Not warned when flagging" so I suppose you will be warned when too many flags are declined but before a flag ban happens. Also I seem to remember to be somewhat smart, that is 5 declined from 30 total flags shouldn't be an issue and should even grant you more flags per day than the average non-flagging user (?).