I don't know if it has ever been addressed in the comics, but the Flash talking has always bothered me as well. He often moves faster than the speed of sound, yet we get lots of situations like the one you described. Suspension of disbelief is required here I guess...
In this particular instance, not in any other mind you, Kid Flash gets his new suit from Red Robin so there may, in theory, be some sort of walkie-talkie (is that what they still call those?) in the suit that allows this.
But in a world where men are made of steel and fly and invisible planes abound, this isn't a very tough suspension of disbelief, as Otter suggested.