In a 240 V "2-phase" wiring, how does current/amps get distributed?
The high currents do pass from L to L, so each of those will see the full current. There may be some small current flowing from one of the lines to neutral for the controls/clock, but that's not important. I'd say that you need at least 10AWG - depending on the wire type and temperature rating - to handle that. FOr 60C rated NM wire that'd need 8AWG.