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The sparks from a sparkler are tiny pieces of burning iron. Where does the oxygen come from that is reacting with the iron?

This depends on the composition of the sparkler. It's entirely possible that it's just reacting with the gaseous oxygen in the atmosphere, as would be the case with most combustion reactions we would typically call "fire." Explosives and incendiaries, such as those initiated by gunpowder, carry their own oxygen within their chemical makeup. 


If the sparkler is a gunpowder mixture with iron filings thrown in for effect, then the oxygen is coming from potassium nitrate,...

This depends on the composition of the sparkler. It's entirely possible that it's just reacting with the gaseous oxygen in the atmosphere, as would be the case with most combustion reactions we would typically call "fire." Explosives and incendiaries, such as those initiated by gunpowder, carry their own oxygen within their chemical makeup. 


If the sparkler is a gunpowder mixture with iron filings thrown in for effect, then the oxygen is coming from potassium nitrate, or "saltpeter." Gunpowder is typically made from charcoal, sulfur, and saltpeter, with the saltpeter acting as an oxidizer (which has a more specific definition, but in this case it means adding oxygen atoms). Adding those oxygen atoms reduce the energy of the compound it forms, and that energy is released in the form of heat, light, and sound. The iron, in this case, is competing with the carbon for those oxygen atoms, so instead of just carbon dioxide and monoxide, the reaction also produces iron oxide, which takes the form of reddish-white sparks when it's hot. 

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