Green’s Dictionary of Slang

1. (US) flippant, insignificant.

1929

M. Levin Reporter 157: A dainty, pink-faced youth [...] drifted in. His flippy way of walking reminded the reporter of Malone. [Ibid.] 274: She was suddenly a flouncing, flippy, free and easy girl of the city.

2. crazy, eccentric.

1957		Jailhouse Rock [film script] ‘You didn’t say a thing about my outfit.’ ‘Flippy . . . real flippy.’.
1971		B. Malamud Tenants (1972) 45: Don’t talk flippy.
1979		(con. 1955–58) Pepper & Pepper Straight Life 177: You’re getting that rep of being a loner and kind of flippy.
1986		S. King It (1987) 740: Don’t go flippy.

3. see flip v.⁵ (1b)