The fossil record indicates they evolved far back in their ancestry from something not dissimilar in appearance to a lobe finned fish, but with an extra pair of bilaterally symmetrical fins, though they now look surprisingly similar to the appearance of the more serpentine mythological dragons of earth.
They have electricity generating organs similar to an electric eels that no doubt originally developed under similar evolutionary pressures for similar reasons but now serve a different purpose, they use it to extract hydrogen from water by electrolysis which is stored in evolved swim-bladders that have now become a series of valve linked chambers storing hydrogen under varying pressure.
Much like some fish they retain both lungs & gills.
The hydrogen can be released through the valves from the high pressure bladders into 'normal' swim-bladders for more buoyancy in both air or water & (if there's time) it can also be pumped back through valves into higher pressure champers through muscle contractions to reduce buoyancy.
If they need to lose buoyancy quickly the swim bladders can be vented through the gills, nostrils & mouth though if in flight the mouth is closed & the nostrils pinched shut much like a camels to avoid slowing their passage with the rapid expulsion of the gas.
The Question : If the animal has a body mass similar to a typical race horse, so about 1,000 pounds, how big do the fully inflated unpressurised swim-bladders need to be to allow the animal to fly by flapping rather than gliding in a similar gravity & air pressure to earth's?