Hmm, from what I remember:
Jinn are supposed to be made of 'smokeless fire' or 'scorching wind' (and they are sometimes described as being made out fire, while humans were made out of clay)
They have free will, like humans do
They can be quite hard to some, something like heat shimmer in the desert
They usually have some way of moving around very quickly.
So something like:
Cloak of Shadows (variant)
Inhuman (or more) speed
toughness against fire
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Then, the more powerful ones (usually called marid or ifrit (afreet, efreet, etc) ) would typically have magic (evocation and/or thaumaturgy) rather than being very much stronger or tougher, though having a higher speed power (and possibly flight) would certainly not be out of character.
Some also seem to have the full range of shapechanging, up to being able to imitate specific people.
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Lesse what else. After Allah made man, the jinn were supposed to bow to Adam, but some (Ibliss, Shaitan), in pride, did not do so and were cursed or cast out or something.
I think this is also where the 'devil on the shoulder' trope came from, as there were supposed to be a faction of these bad jinn who would whisper to people and try to get them to do evil deeds.