This is an interesting discussion, and I wish we had more of this sort of thing on PPRuNE.
Katamarino - good point about summoning help e.g. AFS, rescue etc., there again I would argue for Fuji's point that fire appliances etc. are not much use in the air. Letting someone know where you are is a good idea, however it is a question of priorities.
If there's a funny burning smell or slames start to lick up around the instrument panel any RT would be the last thing on my mind. My own priority would be to fly the aircraft, bring the situation under control and then get on the ground ASAP. Most likely one would be forced to divert into a field, or if the fire had been brought under control, the closest airfield, if it isn't too far away (i.e. a few minutes flight time). If there's been a fire you don't know what sort of damage may hav been done and so I'd want down ASAP. Plus I'd leave all electrics off just in case of re-ignition.
If flying an aircraft with electrically-operated flaps, I would argue it's still not a major issue. Most light aircraft will quite happily land flapless without a huge loss in landing performance. Larger, faster, more complex types perhaps but not C172s etc. A flapless C172 will still get into a field without flaps. If landing distance is really an issue then I'm sure that whacking into a hedge/fence fairly gently at the end of a forced landing is much more surviveable and hence desireable than being burnt to a crisp in mid-air whilst farting about trying to get the flaps down.
I remember an incident with a Cessna in Scotland a few years back - 2007 perhaps? The 60A CB for the alternator tripped, it was then reset and because of a short-circuit it welded the CB closed and caused a fire. They ended up doing a forced landing and everything was OK... anyone have the report for it?