Should a "thank you" comment, for instance Thanks for your answer, be flagged as non-constructive?
If a "thank you" comment is flagged as non-constructive what would the moderator reaction to this flag be? Would it be marked as helpful, or not?
A "thanks" comment that doesn't provide any specific praise about the answer is usually not constructive, and almost always qualifies as "too chatty" as well. However, when the comment says something substantive, even if general (like "Great post! This explains a difficult concept in a very clear way."), it likely has some value and may be a poor candidate for flagging.
You shouldn't feel obligated to flag them when they are not distracting from anything else. When it distracts from other comments (especially if other comments are hidden as a result or take up more than a small fraction of the height of a page), I think they should be flagged. I'm not saying they need to be flagged whenever there are n or more other comments. This is subjective, there probably does not need to be a rule for this, and everyone can use their own judgment.
When such a comment is flagged, it should be removed unless it contributes something. If people have replied to it or it has many upticks, that suggests it may serve some purpose. In any case, almost always when such a comment is flagged, the flag should be marked helpful even if the comment is not removed (with the only major exception being if the comment is not removed because it is useful, and it is frequently flagged, presumably by the same user).
Different site communities may have different ideas about this. You should not be surprised if flags on these comments are handled differently on different Stack Exchange sites.
When there is more than one "thanks" comment (from the same user or from different users), all but one are virtually always both not constructive and too chatty even by highly restrictive interpretations of those categories. In this situation, comments should almost always be flagged and removed.
While I'd prefer it if those thanking in comments would pay it forward, I see no benefit/reason/rationale to flag those sorts of comments.
Flag only the comments that are seriously egregious - offensive, too chatty, or just plain rude.
Flagging friendly comments is silly. As was said above, we aren't robots.
"Thank you" comments (and their equivalent in questions) are fair game when cleaning up or editing something anyway. There is no point in taking specific action because of them. Don't alert mods to something that doesn't actively bother anyone.
There are literally millions of bigger issues (actual problems) on the site.
I guess no need to flag such 'thank you' comments reason being that firstly it is not a major offense which should be flagged and secondly mods are already busy with other site moderating chores.
It would be better if you leave a comment reminding the user who posted 'thank you' that such comments are not encouraged on Stack Exchange sites and upvoting / accepting answer are as good as writing 'thank you'.
Removing flagged comment is a prerogative of the moderator who is reviewing your flag, the mod may decide to remove or leave the flagged comment. There is no official rule on this.
'Not constructive' is the closest flag that can be used in such cases. A 'thank you' note is not rude, offensive, obsolete, or chatty.