It's mostly rote memorization, of course. The top lines for each race are kept current by representatives of each one's tanking classes. For nonsapient species there are research tanks who'll go into the wilderness and imitate the sounds that creatures make to each other until they find one that provokes an instant attack. Undead and demons are brought into special laboratories where calibrated chains measure which insults produce the strongest attempts to break out. Then the results are written down and young fighters chant phrases in unison until they get them right.
Slimes are the worst. Sure, it sounds like a burp to you, but we've spent weeks at a time practicing to get that enunciation just right. And no priest ever puts Pain Suppression on your vocal cords.
It's not just a phrasebook, though. Draconic is easy to pronounce and we've got dozens of different lines to throw at them. The hard part is using the right one. Dragonkin and whelps are part of a rigidly ranked society with true dragons at the top. You have to match the taunt to their social status to truly hit home. Tanks spend long hours watching their instructors pop up portraits of dragonkin until they can peg their rank from any angle. This gets easier as you go up the hierarchy. With Sartharion you only have to quote his adds back at him.
Anybody with a match can set things on fire. Making a demon forget about that tasty warlock he's about to bite into--that takes brains.