Should I just flag it as "Not an answer"? Until the sarcasm started it did contain a sort-of related opinion, although it should probably be a comment and not an answer.
Do you find this post at least mildly offensive as well? Enough to warrant a flag as offensive?
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When the sarcasm is laid on that thick, "not an answer" should be sufficient. It doesn't quite warrant an offensive flag in my mind, but it probably wouldn't get declined either. You can always flag it as "other" and explain what's wrong with a post if you don't think we'll get that it's a joke answer that doesn't really answer the question.
In general, the purpose of a flag is to bring an issue to a moderator's attention, so agonizing over which flag is probably not the best use of your time.
That said, I'd flag it as "not an answer", as to my mind it wasn't intended to actually try to solve the asker's problem. It's mildly offensive or at least annoying, but no, I wouldn't flag it as such.