Of course not. When you flag (downvote) something those rewards are sent back to the rewards pool and are allocated among all authors.
There is no “rewards” earned for the individual flagging.
Currently when you cast a downvote it uses mana from your 10 “free” votes per day. The proposed changes would just make it where there would be a small amount of additional mana for downvotes, that will be separate than those used for upvoting. I hope that makes sense.