In formal and (in their domain) complete theories, one always will have circular definitions. Examples:
F = ma. Try to define mass without referring to a force, or the other way round. (OK, you could do it by referring to Lagrangian, energy, etc but if you look carefully you will see that you always took something on board implicitly you did not define yet, and then, if you do, you will have to refer to a concept you already were using).
Evolution: the survival of the fittest. Who is the fittest? The one that survives...
It is simply the case that definitions of concepts are always circular. It cannot be different. One could even go one step further: every definition is a tautology. And with time it is not different.
But what makes a theory scientific (math excluded...) is that one can make operational definitions. That means, one can define concepts as actions to take and observations to make. In this way one establishes that a theory is about something. In short: conceptual definitions are always circular; operational definitions are not.
The idea of time-flow is more or less just a metaphor. Things flow in time*, or better, processes occur in time. Time itself does not flow. Normally what one means is that the time we call 'present' is ever going onwards. But this is just an example of an indexical. Indexicals are words which meaning is completely context dependent. Examples are 'I' (meaning the speaker), 'here' (the place where the speaker is), and, yes, 'now' (the moment that a speaker utters a sentence). For these do not exist any hard physical references. So the 'flow of time' is not a physical concept. But you treat it as such.
Many laws of physics have a dependency on time: this means that we can describe how things change in time. But for laws of physics to become really empirical we need an operational definition of time. Practically, we do this be using 'standard changers', aka clocks: some regular process, where we can count the number of regular changes (tick-tack-tick...).
And as a final remark: you know that physics just works. One can predict solar eclipses many years in advance on the second, special relativity is tested to the bone and is more or less the touchstone for every fundamental law of physics (they must be Lorentz-invariant), general relativity has until now withstood every empirical test: so there cannot be much wrong with the physical understanding of time.
* On second thought, no, things do not flow in time. They flow in space... 'Flowing in time' is still metaphoric speech.