There are a lot of ionic compounds in fireworks, most of them are salts, like: Strontium Nitrate and Strontium Carbonate ( both in the color red); Calcium Carbonate and Calcium Chloride (orange); Sodium Nitrate, Sodium Oxalate (yellow); Barium Nitrate and Barium Carbonate (green) and so on. For the gunpowder itself we have the Potassium Nitrate as an ionic compound.
The chemical reaction for the combustion of black powder is:
6KNO3 + C7H4O + 2S -> K2CO3 + K2SO4 + K2S + 4CO2 + 2CO + 2 H2O + 3N2
It's not just a single reaction, but this is a general representation of it.