Can charge flow between two points if their potential difference is 0?
Electric current is the rate of charge flow past a given point in an electric circuit, measured in Coulombs/second which is named Amperes. In most DC electric circuits, it can be assumed that the resistance to current flow is a constant so that the current in the circuit is related to voltage and resistance by Ohm's law.
These relations describe electric circuits, i.e. for current to flow continuously there should be a potential difference introduced and an electromotive source which provides the energy. Otherwise the currents are transient.
Like mechanical potential energy, the zero of potential can be chosen at any point, so the difference in voltage is the quantity which is physically meaningful. The difference in voltage measured when moving from point A to point B is equal to the work which would have to be done, per unit charge, against the electric field to move the charge from A to B. When a voltage is generated, it is sometimes called an "electromotive force" or emf.
In this simple circuit we see a voltage difference imposed by a battery on the left. The voltage is the same in the conducting wire ( assuming zero resistance wire) there is a voltage drop across the resistor, and then there is no voltage difference on the return wire. So the answer is , yes, a current can exist in a closed circuit on the the zero resistance wires. It is enough that an electromotive force supplies the energy for the current.
For increments in the circuit where there is no voltage drop Ohms law is undefined, as 0/0, it cannot be used to find the current.
The crucial term is that in a "closed circuit" there must exist a voltage drop, otherwise the problem is undefined. In an open circuit there is not current