Flames out the exhaust is not a backfire. Flames out the carburetor is a backfire. The caller has a late combustion, known as “popping”, where the mixture burns in the exhaust system rather than the combustion chamber.
Flames out the rear indicate a severely rich mixture and a very hot exhaust. Too much raw fuel coming out the tailpipe.
An air leak in the exhaust near the head is a likely contributor of exhaust popping. Without air the unburned mixture could not burn, would cool by the time it exits and not self-ignite.
Lean mixtures often pop on deceleration when the mixture is not rich enough to burn when sparked but eventually burns when it hits a hot exhaust pipe which is exceptionally hot because the mixture is lean (Catch-22). A sloppy weld leaving a tang in the exhaust, or carbon buildup can create a hotspot to ignite unburned fuel that wouldn’t otherwise burn. But this all occurs near the head long before flames out the tailpipe.