Re: Universe inflation : what about the time flow ?

Basically the answer is that "time flow" is part of the equations of General Relativity (GR), which describes how space and time respond to the presence of matter, energy, etc. When we talk about the expansion of the Universe, it's usually in terms of how space looks everywhere at the same time, with "how space looks" consisting mostly of how distances between objects (more accurately, spacetime events) would be measured. The expansion, of course, is that these distances are increasing with time, without the objects themselves having to move through space. Of course, for your question the key phrase here is "increasing with time," but changes in the relative time flow are also accounted for in doing the calculations. Perhaps the main point here is that in GR, time is not a thing which is separate from space, as it is often taken to be in everyday situations.

In principle one could propose a theory in which time is somehow separate from space, and governed by laws beyond GR which may include other effects. However, it appears (to me, at least) very difficult to do this without having profound and easily observable physical consequences. For instance, the spectrum of light observed from very distant quasars matches very nicely with what we know of the laws of physics here on Earth, once we make appropriate GR corrections for the differences in spacetime when the light was emitted, and how it has changed during the light's travel to Earth. Further, it is possible within the framework of GR to generate the observed increase in expansion speed by adding something like "hidden energy", and there are other reasons to believe this might exist as well. So it is simplest to operate within this framework. That's not to say there isn't some other, more complicated effect, but at this point there's no evidence that requires a more complicated theory.