How do Eddy Currents manage to "flow"?
I always thought that in order for current to flow, conductors must be in different potentials.


This rule depends on a couple of simplifying assumptions that taken together are called the "lumped circuit approximation". 

One of these assumptions is that there are no significant changing magnetic fields passing through the circuit. Without this assumption, we can't even actually define a potential at each point in a system.

But there are lots of situations where this assumption isn't valid. For example, in a magnetic generator, the internal working of the generator depends on the assumption being violated, even if we can still analyze the rest of the circuit outside the generator using lumped circuit analysis.

Similarly, eddy currents occur when changing magnetic fields excite currents in the metal. They don't depend on differences in potential because they come from the changing magnetic field, rather than from fields produced by electric charge. And those changing magnetic fields even mean the potential isn't well-defined in the regions where the eddy currents are found.