I don't see any area in my profile that would indicate this, unless I'm just missing it
No, only moderators can see comment flags in the flag queue.
This does exist as an unpopular feature request here.
Generally speaking, the author of a post is never notified of any flag for that post; this means the author doesn't get a notification through the Super Drop-down Collider, or a bar notification, which is the type of notification used to report a new assigned badge.
The author is notified if somebody leaves a comment for that post; in the case the comment has been left from a moderator, the author is notified even after the post has been deleted.
10k users see the list of flags pending for any post, but:
- They don't get any notification in the Super Drop-down Collider
- They don't see flags for comments
- They don't see flags for their own content
- They don't see custom flags
Just to be sure I am using the right name, this is what I call Super Drop-down Collider.