Famously, D. C. Williams ridiculed the deep-seated intuition (at the heart of Bergson's thought, of course) that there is a flow of time, asking how fast time is flowing, if it's flowing. Some wits have tried to respond: "Always at a second per second." But there is a much better and less trivial answer. And interestingly it is an answer that has a home in the B-theory of time.
The Twin Paradox suggests that we should distinguish the internal time of an individual from something like the generally shared external time of the human community. Thinking about time travel suggests a similar distinction, as Lewis has noted. But once we have a distinction between internal and external time, then we can give a non-trivial answer to Williams' question. The flow of time is measured in terms of external units of time per internal units of time. If external time is defined by the shared life of the human community (that's one among a number of options—we should probably understand "external time" in a context-sensitive way), normally time flows at one external second per second. But if I were to engage in travel at relativistic speeds, it could be that in a month of internal time, eight years of external time would elapse. And if I were to engage in gradual backwards time travel, then I would have a negative rate of time's flow: maybe I would be moving at −1 external century per internal second. (In non-gradual time travel, the rate would be undefined.)
The distinction between internal and external time fits best with the B-theory. So the notion of time's flow, surprisingly, seems to have its home in the B-theory.