Flares produce their light through the combustion of a pyrotechnic composition. The ingredients are varied, but often based on strontium nitrate, potassium nitrate, or potassium perchlorate and mixed with a fuel such as charcoal, sulfur, sawdust, aluminium, magnesium, or a suitable polymeric resin.
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LoginThis page has a table showing percentage of stuff in flares from different manufacturers
Different companies use different compositons when manufacturing road flares, so it is impossible to give a specific answer for the flare in your hand. However, they do tend to have similar compositions, and so a generalized answer is possible.
Common ingredients:
Strontium nitrate
Potassium nitrate
Potassium perchlorate
Sulfur
Charcoal
Sawdust
Aluminum flake
Magnesium
Red gum
Epoxy resin
Shellac
Dextrin
Parlon
Note that every composition contains strontium nitrate (Sr(NO3)2). That is because the strontium is responsible for either a red or red-orange color. However, strontium nitrate is not a great oxidizer - a mixture of Sr(NO3)2 and a fuel will hardly burn. So a better oxidizer such as potassium perchlorate or potassium nitrate or an energetic fuel such as aluminum or magnesium is added to give the extra energy needed for a fast combustion.
The rest of the components are either fuels, or a compound that serves as a combination fuel and binder, or parlon which is a binder but not really a fuel.
Some older flare formulations also had things such as pitch, asphalt, wax, tallow, potassium chlorate and black powder. Those are not likely to be part of modern flare formulations.