If I handcuff myself and then get set of fire, will the reflex break the handcuffs?
Well, there’s only one way to find out…
The ‘fight or flight’ response is pretty strong but if your hands are cuffed behind your back I can’t see it happening, the muscles used to move yours arm away from each other in this position are pretty weak.
You might have better luck if you electrocute yourself, the violent spasms of the muscles might do the trick, though still highly unlikely I would say.
WAG… I have to think the breaking point of your hands is less than that of the handcuffs. That alone should prevent it.
Another thread that would benefit from “need to know quickly”.
Maybe instead of “reflex” you mean thermal contractures? As muscle burns the tissue contracts, or shrinks, just like (sorry) meat on a grill. This causes oppositional forces at the joints, as the muscles that extend and flex the joint are shrinking at the same time. All else equal, the larger muscle mass wins. Thus, the arms end up flexed at the elbow, as the flexor muscles (bicep) are larger than the extensor muscles (triceps). For the same reason the wrists also end up flexed to result in the so-called “pugilistic” posture. The force of these oppositional movements can be so great that the bones break, thermal fractures.
Getting back to the OP, handcuffs would probably distort the shape of the contractures, but wouldn’t change the underlying basis. My guess, if you’re using quality metal handcuffs, is that the bones would break before the handcuffs. Further burning and contracture, pulling against the handcuffs, might then cause one or both hands to detach (this can happed by the force of contracture alone), and the handcuffs could then slip off. I think this is more likely than the handcuffs breaking, but I’ve never seen an actual case.
If you burn enough so that the skin and fat and muscle melt off, I’m sure you could slip your wristbones through the cuffs. It would be even easier if reduced to ash.
For centuries, they have burned people at the stake, and they weren’t handcuffed to the stake, just tied with wetted ropes or leather straps. But you don’t hear about heretics escaping because they could break their ropes and flee from the stake.
Because “I’ll be in my bunk” would be wrong? 
Please tell me the OP is just an author writing a book.
Those Vietnamese monks who burned themselves in protest had no reflexes whatsoever. They just sat there is peace as flames engulfed them.
Too many variables here. How strong are the cuffs? $1 Dollar General kiddy kuffs? How big is the fire? If you’re being attacked with a blowtorch could you melt the chains between the cuffs?
Ropes would be worse than a steel chain, however. It is possible (if difficult) to snap steel with the right leverage. Ropes stretch, and if you tie several, they’ll never break under ordinary human force.
I doubt that you could break some real handcuffs, but maybe you can gnaw off your hands. You can wait till they’re well done and crispy if you prefer it that way.