Is there a way to initiate this feature? Sometimes you know comments should be moved but you have to wait until 20 some odd comments come before the auto-move to chat feature pops up. Is there a way to expedite this?
Only moderators can do this. Unfortunately moderation of comments is one of the few things that isn't "outsourced" to the community.
If you feel a comment should be removed then you can flag them. If you want to remove multiple (or all) comments it's usually easiest to just flag one comment or the post with "other" or "in need of moderator intervention" and explain why you feel all comments should be moved.
If you flag just one comment then be sure to mention "I didn't flag the other comments", since in the user interface only the flagged comments are shown (and not all of 'em).