How can I get notified when a flag I raised on a comment has been reviewed? (I don't want to manually check
Flags of any kind are meant to be fire and forget for the most part. You can only find what happened to them if you directly look at your flag history.
Generally comment flags when marked as helpful will result only in the deletion of the offending comment. For the most part if a comment has been removed then we should all just move on.
If you think that more needs to be done e.g. there's a stream of rude or abusive comments from the same user then raising a custom mod flag on the post (rather than on any particular comment) and explaining the issue that way is likely to get better results.