To put it politely, this is asking the inmates to run the asylum.
I believe this would actually make the false/satire/doesn't-conform-to-my-beliefs-so-must-be-fake stories more durable. If it just shows up with a note "this has been flagged false by users" that will do jack all at best. If links flagged as "fake" get removed, then you tweak all the conspiracy mongers into KNOWING the link is true, because it got suppressed.
In all actuality, this would probably just turn into another means of online harassment.