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Part of the total reaction is mentioned here:

$\ce{2KClO3(s)} + \text{heat} \rightarrow 2\ce{KCl(s)} + 3\ce{O2(g)}$

The rest is a mystery. (And where does the heat come from?)

I regret to say that I have delayed acquisition of organic chemistry principles that might have answered this question already but can't help but wonder why, right now.

I feel that once the role of sulfuric acid is cleared up, the reaction with sucrose not described above will explain itself.

(And no I am going to run around burning things down with this knowledge.)

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I think the sulphuric acid isn't really a catalyst here -- I think you use the heat from the reaction between sulphuric acid and sucrose (which will start happily at room temperature) to start the reaction between the potassium chlorate and the sucrose (which usually won't).

ETA: Once you've done that, it's pretty much a straight-up messy combustion reaction, only with the oxygen being provided from a solid source (thermal decomposition of chlorate to chloride and oxygen as the reaction you mentioned shows) rather than anything mechanistically clean. Compare, for example, this fairly typical demonstration just using hot chlorate and a sugar source: Oxidation of Sugar or Gummi Bear with Potassium Chlorate.

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well that's a start I guess – Sadiq Feb 15 '13 at 14:46

A drop of sulfuric acid on the sugar will cause its dehydration. The reaction is highly exothermic and yields a highly porous carbon "foam", blown up by the steam simultaneously released. [You'll find lots of videos of this experiment, more or less reasonably conducted (with/without gloves and proper eye protection), mostly using larger amounts of sulfuric acids.]

The heat of the dehydration reaction will furnish the decomposition of the chlorate, releasing oxygen which, in turn, will start to oxidize the porous carbon mass to carbon dioxide. This reaction again is exothermic ($-394\,\mathrm{kJ\cdot mol^{-1}}$). Sugar might start to caramelize and release more water (as steam), more chlorate decomposes to yield oxygen, etc.

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