My flags keep getting declined

My answer is going to say similar things to what Boltclock has already said in their answer here. I'm posting an answer, rather than just upvoting Boltclock's answer and adding a comment, because I'm the moderator who handled the first two flags you are asking about and one of them is "mea culpa".

The first answer you mention is, barely, an answer to the question. It's not a great answer. I wouldn't even call it a good answer. However, the issues with that answer are the purview of downvotes and/or editing, not flags. While it looks like it may be link-only, A) the question is asking for resources, so links to such resources tend to be answers; and B) the name of the product, Araxis Merge, is actually in the URL, which means that even if the current URL dies, you could still find it from a search. Yeah, it's not clear in the URL, but it is there and would be the first, and probably only, possibility I'd try if searching.

On the other hand, for the answer mentioning "Beyond Compare" and "WinDiff": Yes, I should not have declined this flag. I'm sorry about that. It's really not an answer. At the time, I believe I was thinking that it was mentioning WinDiff, which isn't covered in other answers. I was probably just skimming and felt that the answer could be edited to remove the "thank you" portion and leave just the WinDif mention. That is, however, not what's appropriate for what's there in that "answer". You're right that it is, at best, a comment and an NAA flag is appropriate here. I've converted it to a comment on the original "Beyond Compare" answer.

While I didn't handle the flag on the third answer which you NAA flagged, it is an answer to the question, so NAA and/or VLQ flags are not appropriate. NAA flags are only for things which are clearly and obviously not answers. To report more complex issues, like the fact this answer is, probably, just restating what's in the accepted answer, you need to use a "in need of moderator intervention" flag and include an explanation of the issue (i.e. it needs a custom mod flag). [Note: Actually knowing that it's only a restatement of the top voted answer requires knowing that the only possible entries for "Target Framework" are .NET versions. Without domain knowledge, I don't know that. I consider it a moderately reasonable assumption, but it's not something I know and it's not stated in either answer or the comments on the answers.]

You mentioned that there's an upvoted comment on that answer which provides some supplementary information as to why you NAA flagged. Frankly, comments on the post are commonly not even seen by the moderator when evaluating named flags. Comments are not shown in the default view in the flagging interface. What is shown in the default view is the unformatted first few lines of the post. For named flags, the decision on the flag is commonly made based on that view. The moderator can, of course, get more information, but the named flags have very narrow uses such that seeing more information is commonly not necessary.

The underlying reason that the named flags need very narrow definitions (i.e. why reporting things like the above "late duplicate answer" issue needs to be a custom flag and not NAA or VLQ) is that moderators can't spend the time to do a full investigation of every flag looking for all possible problems that might exist. If we were required to do that, then it would increase the time it takes to process those flags by somewhere between 10 and 1,000 times. It's just not possible for Stack Overflow to have enough moderators for that level of time/effort on every flag. Thus, we need the people who are flagging to do the first pass at sorting issues into categories. The named flags are for things which obviously fit into the class of issues for which the flag is named. Things which don't obviously fit into those categories need custom flags, so that A) we know what you think the issue is (i.e. so we don't have to investigate everything while re-doing work you've already done, and still possibly miss the issue you see), and B) we know that we need to spend the time to take a more detailed look.

Yeah, you're right. The one mentioning Beyond Compare was a thank-you answer with only a tiny bit of exposition that's better suited as a comment. While it qualifies as NAA, I don't think flagging it was the best choice as NAA flags tend to be handled in bulk — if they don't stand out immediately as thank-you or some other form of NAA, the flags are likely to get declined, unfortunately. Even I don't feel confident I would've handled this flag correctly, although I do take the time to read every post (and comment) before handling flags of any kind.

Link-only answers are not NAA, especially when the question itself is asking for links in the first place, and the one that you flagged even provides a short description of what the tool being linked to does. Yes, we don't allow tool recommendation questions because readers have to download stuff from elsewhere for the answers to be useful, but you're better off finding link-only answers to things that aren't inherently link recommendations in the first place.

That last one? Hmm. Yeah I guess 17 non-deleted answers is a lot. I guess it wouldn't have hurt to remove that answer and declutter the question, it's old enough that the author isn't going to— wait, you flagged that as NAA too? That's not right. Late answers are answers, and a custom flag should've been used here. You seem to be using NAA as a catch-all flag for any answers that should be removed for a variety of reasons. NAA is to be reserved for specific types of posts only, so that it can be safely handled in bulk (Stack Overflow gets hundreds of these every day and mods only see a fraction of them). There's a reason it's called "not an answer". Flagging things that are answers contradicts this entirely. So it's no surprise that it was declined in this particular instance. It doesn't matter that someone pointed out the nature of the answer in a comment. It's still your responsibility to use flags correctly.