Are the concepts of 'panta rhei' (Heraclitus' river analogy) and hard
You are taking claims and concepts from two traditions very far removed from one another. And yet your question makes good sense; for in some respect I believe Heraclitus would understand hard determinism, and the modern hard determinist would understand that panta rhei.
Indeed, as that first paragraph implies, I think the better question is not just whether the two positions are logically compatible, but whether they are intelligible to one another. After all, vegetarianism is compatible with belief in phlogiston. Nothing in a theory of phlogiston says you have to eat meat, and nothing about vegetarianism requires you to believe in the existence of oxygen. But this compatibility is surely a trivial one. There is a fuller sense, I believe – if I’ve understood your question – in which you want to know whether these two worldviews are mutually, shall we say, comprehensible not just compatible.
In one direction the mutual comprehensibility is not at issue. Unless hard determinists want to say that change is limited or does not take place (and I can’t see why they would), they would understand the panta rhei doctrine even if they did not often feel the need to announce it. After all, whom would they need to inform that the natural world changes?
But the other direction is the tough one. Would Heraclitus understand hard determinism?
I’ll begin at the end of your original question. You are not interpreting Heraclitus wrongly. But we need to interpret him a little further. According to one view of his theory that has many adherents today, the doctrine of Flux (everything flows; can’t step into the same river twice) is a supporting position in Heraclitus’s total view. It underwrites the more general claim of the Unity of Opposites (every object that has a property P has the opposite property not-P, whether at the same time or in some other respect). And that more general claim, in an obscure manner that hasn’t been fully reconstructed yet, underwrites the grand thesis that Heraclitus wrote his book to present, his Monism, the thesis that “All is one according to some logos or rational order.” Everything flows, to be sure, but everything flows in accord with this logos; and there is a pattern and a structure thanks to which things are identical with their opposites.
All we need right now is this idea of a logos, i.e. the idea that there is a rational order thanks to which things constantly change. For if things constantly change according to some such order, it seems more plausible that they change in determined fashion. Heraclitus could deny the determinism, but he doesn’t say anything that I see as such a denial. Indeed the ancient world was not really worried about determinism until after Heraclitus. Aristotle considers a certain kind of logical determinism; and after Aristotle, Epicurus revises the atomism of Democritus so that atoms not only move in straight lines but also sometimes swerve, thereby making some kind of freedom possible. With Epicurus we have genuine worry about hard determinism. But then Epicurus is writing long after Heraclitus, in whom I don’t see such a worry.