Here's a diagram of a theoretical Greek Fire launcher fitted onto a Byzantize Dromon:
Notice two important aspects of this diagram, pressure and temperature. Even Greek fire had to be heated before it was combustible. Again, like oil, it is not a weapon at room temperature and it would not ignite from a spark or existing flame. In order to employ this weapon, it had to be heated and in order to fire it had to be pressurized.
This is the key point I want to make for flame weapons: they require processing and work (in a thermodynamic/mechanical sense) before they can be employed. So anyone who wants to use incendiary weapons in this world (or any world in which you want to pay attention to such things), is going to have to set up a system more elaborate than a wick and bottle. And even heated oil/Greek fire/etc is not going to be easy to handle and use safely, thus the pressurized launcher. If the history of the boiler and steam engine is any indication, I am sure many a Dromon exploded of its own accord.