The 3 Prong Cable Has Continuity On One Prong, But The Other Prong Has None. How Is The Power Distributed On The Prongs. Specific To Certain Operations, Or In Series, Everything On 220 Amps?

How did you check for continuity? Power is not distributed on cord wires. Two are hot and one is ground.

If cord is unplugged and you don't have continuity between connections and prongs, it is a bad cord.
Center prong connects to center conductor, try all combinations for other 2.
For 2 to go bad is extremely rare.