I'm not going to criticize this piece on toothless's physiology since it's meant to be 'chibi' and therefore has some creative leeway. However, there's a few flaws and weak points related to the animation.
The first thing that jumped out at me was the light source. I realize the flickering light is a stylistic choice on your part but you might want to consider what's actually producing the flicker. The only two I can come up with would be refraction from a source of water or fire, e.g., a candle or torch. If it's meant to be the latter, then I would consider making the light yellowish and localizing the drop shadow. The light also has a few inconsistencies such as the far right side of the tail having light facing the wrong direction and the wings not displaying any reflection at all.
This one is more of a personal gripe but the tail wag does nothing for me. A more snake-like oscillation would have fit much better.
The eyes also seem to be problematic. Either you meant for the blink to be faster (which is an easy fix) or it's meant to be slow. If that's the case, then I have a suggestion that every budding animator should learn. Toothless's eyelids seem to be moving at a constant rate which, to the viewer, seems unnatural. The eyelids need to accelerate over time, reach its fastest point in the center of the eye, and slow down to a close. Imagine a ball bouncing from the ground and slowing to a stop in mid-air. That's the effect you want to duplicate.
Overall, the piece is cute and toothless being toothless never gets old. You just need to work on your technique a bit.