It comes from the name of the ex
Formula One driver
Mark Webber. He was "flying" with the car many times.
He did wheelies, and sometimes he really took off with the car after a crash... and before an other crash, like in Valencia, in 2010.
In his pre-F1 years, he was driving at the Le Mans 24H and
guess what? He was flying with the car. That was a horrifying crash, but he survived without damage, he simply walked away.
So when someone "flies" with his car, he is simply webbering.