To freak out. In a good or bad way. The origin of the word came from the Greek goddess Titflapaine. The creator of the phrase is a young girl named Caitlyn from Wisconsin.
It pretty much means to have a massive spazz attack. Like if you're really craving some cigarettes and your friend won't give you any, and you go all pissy on their ass and then soon, people will be saying, "They was being a complete dick today."
Chris: Give me a fuckin' cig man.
Tony: Nah, this is my last one dickface.
Chris will Flip-A-Tit. And pretty much beats Tony's ass to the floor.
To overreact in a womanly or girlish manner, at the most minuscule and/or stupid thing. The term comes from the flipping motion of the persons boobies when they freak out in their titty flipping session. The origin of the phrase came from when a girl overreacted and got all hissy bitchy from the accidental flippage of her titties.