The "flip side" was originally the term for the B side of a 45 rpm record. Forty or fifty years ago, "single" 45 rpm records would have the title track on Side A and a lesser known track on Side B. You had to flip from Side A to get to the second track, hence the "flipside" of the album.
"Said he'll see me on the flipside... of this trip he's taken for a ride, He's been takin'... too much on... off he goes with his perfectly un--kempt clothes."
As '50's slang: You turn my record over, baby. Like, on the *flip* side. (See "flip out" = "go crazyover, freak out over, be turned on by someone or something.")