As far as I understand,
Inside a generating battery cell, electrons flow from cathode to anode. That is, traveling from the anode = positive terminal of the battery towards the cathode = negative terminal of the battery.
Outside a battery = in an electric circuit, electrons flow from anode to cathode. That is, exiting from the anode = negative terminal of a battery into the cathode = positive terminal of the battery.
In other words:
Electrons inside a generating cell flow towards the oxidation negative anode electrode and out on negative terminal of the cell to (-) circuit cathode, performing work and exiting by the circuit (+) anode back into the reduction positive cathode terminal of the generating cell.
e--> K to A inside cell
e--> A to K outside cell
Messy, uh ?