Flames Kits:
Flamer kits (in my opinion) are just a crap product for the Max Power generation. A spark plug is fixed into the tailpipe and I think an injector goes there too. Once switched on, the injector and spark plug make flames. What a stupid idea - anyone can make a fire with the three properties!
Real Flames:
Although most people believe natural flames are produced by a rich mixture, it is quite the opposite. When the car reaches high revs but the throttle is shut (or close to shut), the A/F mixture will be very weak, so week infact that it is not volatile enough to ignite in the very short space of time it is given (due to high revs). Instead, it moves through to the exhaust and the fuel builds up there. Once there is enough fuel, it meets the oxygen outside the tail pipe and - BOOM! Flame(s)!
This effect is enhanced on turbocharged cars: As the throttle is snapped shut for a gearchange there is still some pressure in the inlet manifold, so a touch more fuel is added (in proportion to what the air meter says), but if this is still too weak, the same thing will happen, only there is more fuel there to ignite.
As BenR correctly said, flames will not occur on a car with a CAT (unless you fit a flamer kit with a fuel supply) because the CAT will attempt to treat the unburnt fuel and break it down into harmless elements, so by the time it reaches the outside (or the poxy flamer kit) it will not be a combustable fuel anymore.
Hope this helps - Laurence.