A Run action represents an increased physical exertion when compared to normal movement. This is not possible when using magical flight - you either have your magical "forward" button pressed or you don't.
The reason Charging still works is that the important part of a Charge is taking advantage of the momentum of two consecutive straight-line move actions, which still accumulates. It doesn't require the speed of a full-out Run (Fly still allows you to cover two move actions' worth of distance in a round, anyway).
There is no rules basis for this, but I find the explanation plausible.