Green’s Dictionary of Slang

(US) a jot, an iota, nothing at all; thus couldn’t give a flip.

1969		in Playboy Dec. 102: I couldn’t play worth a flip [HDAS].
1999		Dandy 18 Sept. n.p.: Blummin’ flip. Can’t get any worse.
2005		J.E. Lawson Last Burn in Hell 23: Sorry, dude, I don’t give a flip about the Internet.