Green’s Dictionary of Slang

(orig. US teen) to dismiss or reject; also as imper.

1939		Goodman & Kolodin Kingdom of Swing 193: I suppose I should have given him some kind of a right answer, but that burned me so I probably just fluffed him off .
1943		Chicago Trib. Graphic Section 26 Dec. 7/1: Jive Talk [...] He fluffed her off — he broke off with her.
1953		E. Reid Shame of N.Y. 167: [I]nvestigators who looked into his activities got no help from him. He simply fluffed them off.
1967		F. Sargeson Hangover 53: Tell the world to go and fluff off.
1993		R. Firestone Swing, Swing, Swing 285: When a reporter summoned up the nerve to question Benny himself about his future, he fluffed off the suggestion that he was planning to retire.