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.