I realise that I have given some partially contradictory explanations regarding dragon flight so it's time to set the record straight. Let's start with pure canon, things that were revealed in the strip:
- Dragons are very light to help them fly (comic #34)
- Dragons cannot fly without flapping their wings (comic #359)
- Physics are involved in dragon flight (comic #360)
- Dragons learn to fly only after they learn to breathe fire (comic #388)
Now combine this with the last bit of this ancient blog post
and you get pretty close to a solution (this information will be written into a dragon species article that I will, eventually, add to the background pages
Physiologically, dragons are built very lightly. Their bones, scales and in fact most of the rest of them, are made from very lightweight (but strong) materials that do not form naturally but only through fire magic, which dragons have a great deal off, since their primary element is fire (if you read the creation myth
you know that the first dragons derived from the ancient gods, as such they are in fact brothers and sisters to the World That Is and contain elements the latter does not). Their natural affinity towards fire and fire magic gives them a great deal fo control over this force which they can use, amongst other things, to combust air (breathe fire).
Dragons also have very big lungs (the better to fry you with, dear) and they can superheat the air in there to make themselves lighter yet (like a balloon). This brings their weight/density within the range that they can use their wings to fly. On top of this, dragons will sometimes use magic to improve their speed and maneuverability (dragon magic is strong, and gets stronger with age).
It should perhaps be noted that the whole firebreathing thing is a side effect of flying. The main use of it is to expell the super-heated air from their lungs so they can go down (like a ventile on a balloon). However given the usefulness of being able to fry anything, many dragons have evolved a second, much smaller air chamber where they can compress or store the hot air so they can breathe fire without losing altitude (and vice versa). Flames from this second chamber tend to be a lot more violent due to the compression.