Green’s Dictionary of Slang

(US) a confidence trickster; a crooked carnival game operator.

1953		W.L. Alderson ‘Carnie Talk from the West Coast’ AS XXVIII:2 116: flattie, n. Operator of a flat store.
1961		J. Scarne Complete Guide to Gambling 524: When the flatty is going for the money (cheating), his percentage of the money wagered is 100%.
2001		‘Randy Everhard’ Tattoo of a Naked Lady 5: Carnies got a word for a crooked game operator like me. They call me ‘flattie’ cuz I’ll flat-out rob you. [Ibid.] 6: The Laff Riot carnival was a flattie’s wet dream.
2012		W. Keyser ‘Carny Lingo’ in http://goodmagic.com 🌐 ‘Almost all of the carnies don't like the flatties because you can't win at their game and they take people for lots of money’.