how can the flexplate, or flywheel or whatever you're using, cause a change in ignition timing? Ignition timing is handled by the distributor which is geared off the cam. Whatever is hanging on the either end of the crankshaft will not affect ignition timing.
it's most likely heat soak in the carb causing a mixture problem,
next time it happens manually close the choke on the carb and see if it fires,
if it does then your float level is too low and/or your idle mixture is too lean.
Aside from that, when it doesn't fire when hot just to rule it out and i would check this first, pull the wire going from the ignition coil to the distributor at the distributor end, and hold it about 1/8" off somewhere on the intake or thermostat housing which is clean metal to provide a good ground, have someone crank the engine and see if you get spark. If you don't then that's the problem, or another problem. Hold the wire with a rag or glove so you don't get shocked. If you get spark then reconnect it and close the choke, if that works then it pinpoints the problem to the carb.