Just a random thought. Brewmasters use Breath of Fire. Which I am guessing is done using similar methods to people spitting fire in real life. Meaning they spit flammable alcohol from their mouth through a flame to ignite it.
On other notes. If they didnt have the means to ignite it, they are just spitting mouthfuls of booze on enemies. Which is quite funny.
They breathe magical fire, similar to dragon’s breath.
Brewmasters carry around a cigarette lighter, obviously.
No, no, no. They have nostril hairs that burn like an underground coal fire.
A gentle out breath from nose ignites the spray.
Magic…pffft. Imaginary stuff of lore….now nostril coal fires are real!! 
Like this!
Monks obviously have some amount of magical ability since they can do things like Jade Lightning. I imagine that the principle is the same as irl fire breathing since the move is exclusive to Brewmasters and that they use magic or chi to perform the actual ignition.
We’re just THAT drunk.
Matches?
They are not savages, ya’know!
A Zippo.
They do carry around alcohol. The rest can be rationalized.
They may very well be so drunk that their breath emits enough alcohol vapor to ignite if they use a flint and steel in front of it. It could also be rationalized as chi.
But this is a game in a magical setting, so it doesn’t matter too much.
Hand seals, just like Naruto.