OK, now its clear that you only have one carburetor (my mistake, not yours).
If we adopt my mantra of "Its never the carburetor", then its time check everything else besides the carburetor.
It could be as simple as one lifter is set too tight, preventing a valve to close.
I would start by removing one spark plug at a time while the engine is running. You will find the offending cylinder when the removal of its spark plug causes the backfire to stop.
If you introduce air at the spark plug hole of the offending cylinder while both valves are closed, you will be able to hear air escaping through the carburetor if the intake valve is set too tight.
Remove the valve cover and see if backing off the rocker arm screw stops the air leak through the carburetor.
