Alchemist's fire is a liquid that catches fire when exposed to air, yes. When you open the bottle, the reaction starts. There is probably a little geyser of fire when the bottle is opened. If you're holding the bottle, you'd probably receive splash damage, and immediately drop the bottle, that falls on the floor and breaks. maybe a save to avoid more splash damage?
The thing i wanna know is, if the substance catches fire when exposed to air, how the heck do you make it?
Two or more non-volatile components are mixed together in the bottle. Only after they have had a set amount of time to complete their alchemical reactions to one another does the mixture take on its special qualities. By then, the bottle has been sealed. Hopefully
Or maybe the mixture is prepared and sealed and then must be heated, chilled or shaken (butterfingers!) to catalyze the reaction that creates the alchemist's fire.
The real issue is does every bottle come marked with an expiration date?
What about a born on date?
Depending upon what the composition of alchemical fire is, it may be mixed under water or under oil, or alchemist may have come up with a cruse, primitive vaccuumm chamber.
As a graduate student in chemistry - it really is not all that hard. Don't forget, alchemists are supposed to have laboratories and I would presume the appropriate equipment in those laboratores.
It would be as simple as setting up something similar to a vacuum pump that is operated by suction (in that day and age, probably by mouth ).