This is a fantastic question, just like the Hindenburg zeppelin, Jupiter is about 90% hydrogen so one would expect it to be very flammable!

Answering it requires chemical understanding of what fire is. Fundamentally, flames are just heat and light you see as a result of a chemical reaction called combustion. All combustion requires two components, a fuel (usually hydrogen, carbon, or a mix of the two, such as wood or candle wax) and an oxidant, typically just oxygen naturally occurring in air. This is the reason you can't conventionally have a fire in space. While Jupiter is mostly fuel, it also lacks oxygen (or any substitute) for a combustion reaction to occur. You'd have to constantly supply oxygen to burn anything in space and igniting Jupiter would required impossible quantities.

In comparison, the reason the sun (which is similarly mostly hydrogen) is constantly "burning" (though not quite on fire) is that it's undergoing a constant nuclear reaction, another type of process entirely.