The Apple Don't Fall Far From the Tree

With the ignition on but before starting, you should see approximately three amps discharge. No discharge? There is an open somewhere in the circuit. Check the points first, as they are most likely to be problematic.

Three amps discharge as per normal? Crank the engine. You should see the ammeter flutter as the points open, stopping the current flow, and close, starting it again.

No flutter? The points are shorted to ground somehow (likely), or the system is shorted elsewhere (less likely but certainly possible).

Meter reading normally in all cases? In all probability the points, coil primary, and condensor are doing their job and the problem is likely to be elsewhere.