Is this true "electrons flow from the positive terminal to the negative terminal inside the battery by chemical action"?

The statement "electrons flow from the positive terminal to the negative terminal inside the battery by chemical action" is FALSE.

Inside a battery, there is electrolyte (solution or paste of solution containing mobile ions) between the two terminals. Actually, there is no electron flows in the battery because there is no electron flow in solution.

At the negative terminal (anode), oxidation reaction occurs to release electrons. In the external circuit, the electrons formed at the negative terminal move to the positive terminal. At the positive terminal (cathode), electrons are gained from the external circuit and reduction reaction occurs. In the whole process, there is no electron flows in the battery. Electrons only flow in external circuit.

The description is more a model of how the current flows -- using Ohm's Law, current is from the positive to the negative (or more precisely between an area of high potential to an area of low potential -- like water flowing downhill).

This is equivalent to electrons moving from the negative terminal to the positive one, outside the battery. But, in reality, the electrons don't move in quite that way -- it's more like an induction, as in static electricity.

Anyways, if the flow is from negative to positive outside the battery (through the connection, to do the work), the connection inside the battery would seem to be electrons moving from the positive to the negative, but it's not really chemical action.