No, but it is hard to see this because the difference in our time-frame of reference is so small. There isn't an actual universal flow of time (at least, I haven't heard any good arguments for one).
Take this for example. As I approach the speed of light in my new rocket, time flows normally from my perspective. If someone had eyes fast enough to watch the clock on the outside of my rocket as I passed by, though, they would see it ticking slower than theirs.
A problem I have always had with this implication of special relativity is "what if he goes backwards at the same speed following the same path... Will his time-frame of reference revert to 'normal' - that is, in sync with the observer's?" The answer is no, I think. This is because to say he is going backwards would imply there is a forwards. I can't get the wording quite right so try to bear with me (I've never been a good linguist).
The standard model of cosmology says that the Universe was a point at the Big Bang. It also implies that there is no center of the universe and thus no way to find an 'absolute motion.' Only motion in comparison with other objects within the universe apply. Since the universe expanded from a point, it would also be true to say that the center of the universe is here, there, and every other point in the universe. But there is still nothing to use as a benchmark for 'absolute motion.' The same could be said for time. Photons do not age at all since they travel at the speed of light. The photons reaching the Huble Space Telescope from galaxies ten billion light-years away have not aged at all.
We can't go back in time. But what if we can slow our clock until the other clock catches up, then go at the same velocity? If we did that, sure, the clocks would agree, but that doesn't mean they found the 'universal flow of time.' If they both sped up, their clocks would still agree, and whos to say that they aren't stationary and the whole world is moving instead, anyways? This is the beauty of special relativity - it puts all frames of reference on an equal footing at constant velocity. For accelerating frames of reference, General Relativity holds the answer.
I've thoroughly confused myself, butI hope I kinda sorta answered your question.