I recently flagged this answer as "not an answer", which was declined with the argument " flags should not be used to indicate technical inaccuracies, or an altogether wrong answer".
While it is indeed the case that the "answer" is incorrect, that is not the reason that I flagged it. I flagged it because it doesn't address the actual question, and serves only to question one of the other answers. As such, it should be a comment to that question, not an answer. Basically, I'm 99% sure that the mod was incorrect in declining the flag.
This leaves me with a problem. My only recourse is to re-flag the answer, which is unlikely to help if the same mod handles the new flag. The ability to add a comment to any flag type (not just "moderator attention - other" flags) would help in this regard - I'd at least be able to explain to that mod why I flagged the answer.
However, I'd like to suggest that a better alternative might to to allow declined flags to be re-opened, with an optional comment attached explaining why I disagree with the mod. This means that the current close dialog can stay as-is (I'd agree that a "not an answer" flag shouldn't need a comment), but there is the ability to add comment to a flag if necessary.
To prevent mods being swamped by flags that keep getting reopened and just won't go away, the reopen feature might be limited to a small number of uses (just 1?) per flag, could only be available to users over a certain rep threshold, or could be limited to a single use per flag per day.