SE has specific flagging reasons, not to make it possible to flag (we already have that with custom flags), but to give guidance on valid reasons to flag.
The "Not an Answer" flag comes with a description that implies its proper use (which I suspect that many people don't read or simply ignore):
This was posted as an answer, but it does not attempt to answer the question. It should possibly be an edit, a comment, another question, or deleted altogether.
In other words, the OP is trying to add additional information to their question in an answer, someone is trying to communicate with another user in an answer, someone is posting a new question, or someone is posting nonsense.
"Not an Answer" flags are widely abused to mean "wrong answer" or "I don't like or agree with the answer". This is a problem for the Review Audits algorithm, because sometimes it gets things wrong when moderators dismiss such flags as helpful. It is also a problem for the mods, who now have to take extra time to figure out what is really wrong with the post, take the appropriate moderator action, and then decline the flag (it also modifies their workflow, since they are declining a flag in contravention to the moderator action).
Perhaps it is time that, instead of hinting at the correct uses of Not an Answer, we should simply spell them out, and leave custom flags for the remaining cases. So our flagging dialog would now contain these specific radio buttons to choose from:
- it is spam (an unsolicited commercial advertisement)
- it is offensive, abusive, or hate speech
- it should be edited into the question
- it is an attempt to communicate with some other user (should be a comment)
- it is a new question
- it is not in English, cat on keyboard, or other nonsense
- other (needs ♦ moderator attention)