The act of not wearing underwear, for females. Just as mud flaps behind the wheels of a truck flail wildly in the wind, a saggy vagina may mimic this flapping motion without the restriction of underwear. This is the alternative to "free balling" meant for female use only.
"Dude, it's my laundry day, so I'm mud-flappin' it today."
When you are having anal sex with a girl and you pull out and put it into her vagina.
Friend #1: I was have amazing anal sex with that filthy little filly Stacy and I pulled it out and put it deep in her bum, straight mud-flappin' bro.
Friend #2: Amazing, pure class.