Faulty Circuit Breaker? If not, why the flames from the fan?

Not always. It sounds like your wiring burned up. If there is not a lot of load on the circuit it's possible for the wire to catch on fire and not trip the breaker. Breakers will only trip when the amperage exceeds their rating. If the wire is still intact and not shorting to the case it will not trip the breaker. I had the same thing happen to us on a job friday.

I would turn the breaker off, test and ensure the power is off, then remove the light that had flames shoot out of it. Chances are there is a wire in there that is blackened. If there is you can look into buying a new light kit. If you feel you can do it safely and you can get enough wire on each side of the burned part, you can try **** splicing a new piece of wire in. If the inside is all burned up the safest thing would be to replace the whole light kit or fan.