I couldn't find your song, but I found some interesting "cognates":

Tennessee Ernie Ford's song BLACKBERRY BOOGIE (1952) contains the words

"I fill my bucket right to the top
It makes my lips go flippety-flop"

Uncle Dave Macon's song I'VE GOT THE MOURNING BLUES (1926) contains the lines

"A big honey biscuit and a mutton chop
Will make a n****r's lips go flippity flop." [expurgation mine—JD]

I also found an old advertising slogan:

"Hamburgers, hamburgers, hamburgers hot,
Onions in the middle, pickle on top,
Makes your lips go flippity flop."