EDIT: Updated version. The dissipation fits the beam a bit better now, avoiding the parenting issues on the circles
Also uploaded it on ArtStation here, with a breakdown and the main texture atlas
First WIP of a stylized dragon breath beam attack
Still a long way to go, but a decent start
I like the buildup and the flames tracking the head.
The build up and actual blast is nice, but it ends weakly. I feel like there should be a few lingering bits of flame after the beam shrinks away, maybe even a little smoke out the sides of the mouth. You’ve clearly got a little bit of flame in the mouth during the blast which seem out of place as they’re animating so slowly. I’d pull those completely or speed them up while the blast is going and then have them play at the current rate with some small velocity forward when the beam goes out.
Dayum man, this is (dare I say) fire! 
Especially enjoying the flash and your shapes. 
As bgolus mentioned above, adding some lingering elements could help improve it all. For now, it seems to end abruptly and lacks some of that flavor you’ve got in the rest of the effect.
Can’t wait to see where this’ll end up!
Thanks for the feedback!
I added a few lingering shapes, but I think i might need a bit more. Still think it might be missing something after it ends. Also added some more elements to the beam itself and the “muzzle”