Browsing a bit, I found that this stated in our Help Page. Extracting from it:
When should I comment?
You should submit a comment if you want to:
- Request clarification from the author;
- Leave constructive criticism that guides the author in improving the post;
- Add relevant but minor or transient information to a post (e.g. a link to a related question, or an alert to the author that the question has been updated).
Therefore, anything that does not fulfill any of those characteristics is either obsolete, chatty, or otherwise unnecessary.
Even more relevant to the question stated in this post is the following part (again from the Help Page):
When shouldn't I comment?
Comments are not recommended for any of the following:
- Suggesting corrections that don't fundamentally change the meaning of the post; instead, make or suggest an edit;
- Answering a question or providing an alternate solution to an existing answer; instead, post an actual answer (or edit to expand an existing one);
- Compliments which do not add new information ("+1, great answer!"); instead, up-vote it and pay it forward;
- Criticisms which do not add anything constructive ("-1, see previous comments you scallywag!"); instead, down-vote (and provide or up-vote a better answer if appropriate);
- Secondary discussion or debating a controversial point; please use chat instead;
- Discussion of community behavior or site policies; please use meta instead.
So, to answer the question Should we flag comment-answers under existing answers as rude or abusive? I think yes, as they are by definition otherwise unnecessary and also out of place.
I think that this is a good guidance to when and how to flag a comment, and also when should one refrain from commenting and post an answer instead.