The ‘river of time’ is actually the river of change (the only real evidence of Time flowing is change). Time (in this context) is merely a collective noun.
And we all change…continually. So we change, with everything around us changing.
But we all change independently. Change is reference frame specific.
So the big collective flow (Time) and the indivudual events (from quarks decaying, atoms vibrating, life breathing, earth spinning, universe expanding…depending on reference frame) have their own specific ‘flow’.
Er, no. And the answer lies in your question.
In the first part of your question you very rightly call Time the flow of change.
But in the second part you revert to talking about time flow.
Fundamentally all there is is quantum change-events. They are the tangible reality. Time is merely the (non-specific) collective word for all that change.
Let me give you another example of a non-specific collective word. Traffic is the non-specific collective word for vehicles. We talk of traffic moving, slowing, stopping etc. Yet traffic merely references the underlying reality which is individual vehicles. Individual vehicles are the underlying reality. Vehicles move, starts, stop.Traffic is merely a collective noun.Traffic only ‘flows’ as the aggregate/ average speed of the underlying individual vehicles.
So too Time. Time is merely the collective noun for the underlying reality of change-events. .
So the first half of your question encompasses that understanding, i.e. that it is individual change-events that matter.
But the second half reverts to expressing Time as a tangible entity itself. Fundamentally its not. Its the individual quantum change events that are the reality.