First point that should be made is that you can’t shoot flames if you still have a catalytic converter in the exhaust system, and trying is a very quick way to destroy it. Anybody you see popping flames out the back has already removed their catalytic converter
Two things (outside of the obvious flame thrower kit) can cause flames to shot out the tail pipe.
1. When a motor bounces off the rev limiter, some ECU's cut spark. This causes fuel to load up inside the exhaust. When the ECU apply spark again it ignites the vapor inside the exhaust causing the flames you see. This will happen several times rapidly. You can tell this kind of burn by a series of rapid flames coming out the tail pipe.
2. This one happens when the BOV is vented to the atmosphere (post-AFM, MAF, ect.). This cause’s un-metered air to be released each time the BOV is opened (at each shift). The engine doesn’t know this so it is still applying fuel for the air it thinks is still there, causing and ultra rich condition. The cylinder basically loads up on fuel. This fuel can't be all burnt (for various reasons) before it's all pushed out into the exhaust where it will finish burning. This kind of burn is seen as one giant pop out the tail pipe, after a shift, basically it’s a backfire.