Originally, the other, not-usually-played side of a 78-rpm phonograph record. From way back in the day, whenever it was that two-sided phonograph records became popular.
Let's hear the flip side of that record.
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.")