In Dark Sun, fire elemental clerics were often charged as part of their pact with the elemental lords to promote the growth of forests, fields, and cities - so there would be things to burn.
I think it would depend on the personality of the elemental being. If you're looking for minor sacrifices, such as those a spellcaster would make in order to summon it, burning rare things (particular incenses, woods, oils, etc) would be the obvious thing. If you're looking more along the lines of short-term goals, it would be to burn things by itself. For deeds a long-term servant would perform, it would be more like the elemental pact above.
Of course, there's also the possibility that fire is just part of Fszzzt's toolkit, and not something that is necessarily its goal. For example, efreeti don't seem to be overly concerned about burning things, they're more about establishing domination over what they see as lesser creatures. For novelty, you could go a similar but different path with Fszzzt - perhaps it is interested in kindling the flames of passion in mortals, or fanning the fires of freedom among slaves, or something like that.