I'm not sure what he means by "flow of time" but I don't think he meant what you argued against. I think he's arguing against the notion that time is like some sort of continuum like a river, or like an axis on a map.
I got the same impression. People are assuming that by 'flow' he means uni-directional, as in the arrow of time. He is talking about the fact that 'flow' semantically implies something that moves, but movement itself requires time. So to say that time flows would be circular reasoning.