Re: Warning: Pet Peeve ahead.
He can run fast enough to travel through time and dimensional space and so forth, and I believe lightspeed is the given threshold for that. There's an issue of JLA where they go off to Rann to save the day from an evil space invasion and Wally loans Superman enough speed to outrace a Zeta Beam. As for time dilation, I have three words for you...
THE SPEED FORCE.
Any time anybody brings real physics into the Flash family discussion, the answer is THE SPEED FORCE. Your puny human fizuks mean nothing here!
(And no the THE SPEED FORCE is not magic, it is totally different and betterer and scientifical like unstable molecules and the Phantom Zone. So there. Nyah nyah nyah.)
ps- I have no annoyance with the fizuks majors or the relativity. Science is fun! It just doesn't apply here. (Now I am tempted to work the Speed Force into Creationism somehow...)