Dragonkin are slow, with medium high hp and very high short range DPS. Since you can outrun them, go for them last after you've taken out the faster enemies -- I usually find the dark zealots that often accompany them to be a bigger problem with their powerful ranged poison and lightning attacks. Ember mycon are very similar but slightly more problematic due to their ranged mana draining attack.
Even with high fire resists, I don't think the game intended destroyers to go into tanking battles of attrition with dragonkin unless you like burning through health potions. That leaves you with two options: kill them before they can start attacking (probably requires high offense build), hit and run (lots of clicking, not my favorite play-style), or ranged attacks.
Anecdotal personal experience: A Spectral Echo build on very hard with some knockback, and the occasional titan stomp allows destroyers to take out whole crowds of dragonkin. You don't get the mana/life steal benefits from the echo waves, but in return you take almost zero damage because spectral echo outranges the fire breath. Spectral echo can stack up to 3 times since its cooldown is 1/3 as long as its duration, so you can do 90% DPS even with only 1 point invested in it, and you can upgrade spectral echo to over 80% DPS, allowing it to stack to over 250% DPS with 3 casts.