When energy flows from a hotter subsystem to a colder subsystem the entropy of the combined system increases.
So if they exchange energy in a way that conserves energy then we get $-\Delta S_1<\Delta S_2$ and the total entropy increases.
This does require that the systems have a temperature. If they don't you can try breaking it into regions that each have a temperature and see if you can apply the same idea locally.
This requires that energy is conserved. Energy is frame dependent so you might need a global frame so each subsystem can have an energy. This doesn't always happen. And then you want energy to be conserved between the two, this also doesn't always happen even if you pick some frame. General Relativity would be a common culprate.
And to get the total entropy to increase we assumed the entropy of the system was the sum of the entropies of the parts. This is not always true it comes from the assumption that allowed states for the system are products of states of the subsystem and if they aren't independent enough this isn't always true.
But it becomes hard to call them separate subsystems on those cases. But it was a difficult line anyway since we want them to interact.
You could instead model the entire system as a whole and make new ways to study it based on assigning properties of the subparts. But this is then a different subject matter. Plus an objective description of the whole can be very different than the subjective descriptions parts make about other parts so it might not be wise to use the same words.
However, I think the above equation is intended to explain why energy spontaneously flows from bother to colder (even when that makes the colder thing colder which happens regularly in gravitationally bound subsystems) and that it does so like an entropic force, the energy has many more interactions that increase the entropy than don't and that in the situations where there are temperatures defined this results in heat going from hotter to colder.
So I think most people take the entropic force as primitive and derive other things (such as heat flow) from it. Not the other way around.