Exhaust backfire is almost always ignition related. Always best to diagnose while the problem is present. Have your spark tester and volt meter ready when it happens.
Double check the points gap, check the distributor shaft for side play, it must be tight or the points will not stay set. Be sure the centrifugal advance is free and working. The rotor should turn a few degrees CCW then spring back when released. If it won't turn or is sluggish to return, or does not return, the distributor will need to come apart and be inspected, repaired and lubed.
Do try an old condenser.
Feel the coil when it falters, it should not be excessively hotter than the surrounding metal parts. Be sure it has the proper coil or coil/resistor if it has been converted to 12v. If the coil has been replaced, go by what is written on the coil, not what was on the box or what the counter man sold you.
Check voltage at the coil, or before the resistor if equipped. It should be near battery voltage. Often ignition switches get weak due to exposure to weather. Move the key and see if the problem replicates.
The final test is to have a 1/4 blue hot spark at the plug end of each wire.
Once the ignition system is checked out, move to the fuel system.
Intake backfire is commonly caused by retarded ignition timing, lean mixture, or exhaust valve not opening.
Be ready to check the fuel flow through the carb when it acts up. There is a drain plug in the bowl. With the engine off, fuel valve open, have a clean glass ready, remove the plug, catch the flow in the glass. It should have a full flow, not slow to a drip or stop. This is the true test for fuel delivery.
Places to check, there should be a screen in the fuel fitting at the carb, a screen above the sediment bowl, and a screen inside the tank. If an inline filter has been added it may be the problem. They don't play well with gravity systems.
Look at what was caught in the glass. If there is water on the bottom, rust flakes, dirt, the tank is contaminated and the same will be inside the carb.
A rust flaking tank will be an ongoing problem. The best solution is a new tank if it has not already been replaced.
Once everything has been corrected, the carb may need to be eased apart and cleaned, even though it has already been cleaned, contaminated fuel will carry debris back into it, easy to clean, no kit needed just be careful with the gasket.
Then the main jet can be adjusted. To adjust, start with the main adjust screw about 1 1/2 turn off the seat. With the engine up to operating temp, air cleaner clean (including the wire mesh inside the canister), valves adjusted, thermostat installed and working, choke fully open, ignition system properly working and tuned, In other words, the last thing you do!
Let the engine idle down, suddenly fully open the throttle, listen to the response. Start turning the main adjust in 1/4 turn at a time, repeating the test until the engine falters on acceleration.Then start backing the screw out 1/4 turn at a time until the engine will accelerate without hesitation. A single puff of black smoke it the goal.
Let us know what you find!
