Both the Flash and the observer stationary on the racetrack would agree that he was running ar 99.9%$c$. Where you have, as you often do in relativity, two observers in different inertial frames they must agree on their relative speed $v$. You can see that broadly from symmetry, the two are equivalent so how can one speed be greater than the other? They may disagree about the sign, of course: the observer will say the Flash is moving forwards with speed $v$, the Flash will see the track and the observer moving backwards with speed $-v$.
The observer says he travels 100m in 0.33 microseconds. The Flash's clock will run slow by a factor $\gamma$ so he will say it takes a much shorter time. But he will also see the 100m track, from start line to finishing tape, which is stationary in the observer's frame, shortened by the Lorentz contraction by exactly the same factor, so when he computes distance over time the factors cancel and the speed is the same.