Check the spark at spark plugs, as said. If you have good spark, see if gas squirts in throat of carb. Fix it BEFORE switching to Pertronix. Nothing wrong with a points ignition.
Sounds like carb is filling up during cranking, then it starts, but pump or blockage or gas cap vent or carb internals can't keep up with load/driving.
The bowl will last less than 30 seconds. A pump flow test would be appropriate.
Think of anything else you may have done and forgot.