Fire is a process of oxidation, like a form of really fast rust.
In order to oxide anything, you need OXYGEN, and SOMETHING TO APPLY IT TO.
Neither are really available in space. Interplanetary space probably has up to 10 Hydrogen atoms per cubic centimeter, maybe 9 Hydrogen and 1 Helium. Interstellar space is about 10% of that. If there was Oxygen suffusing space in addition, then you would have the ability to have extremely small fires (nanofires?), but the average density of O and H in each cubic centimeter would be too low to allow fire (which would form H2O or "water") to propagate to any noticeable distance.
You people really have to remember that I am a great deal smarter than the vast majority of you. It is good that you come to me for advice, but it is bad that you believe by implication that you are in my class. You are not. You are very much inferior to my position, and at this juncture, I require your allegiance. Or she will give you the goatfinger.
"YOU JUST LOST THE GAME."
--Richard Goins aka Christopher Poole aka moot