Well, fire-breathing without burning yourself is obviously possible. In addition to various systems already proposed with binary compounds, I'd like to point out that you could have self-igniting saliva that includes a stabilizing compounds. This IIRC is the method many poisonous snakes use with their poison. They simply secrete the anti-dote together with the poison and it will protect them from incidental exposure, but when the venom is "used properly" the protection will fall short and the target will be poisoned.

As the saliva glands -> venom glands path is the logical pathway for the evolution of fire-breathing reptile this would be the proper starting point IMHO. Poison could be initially an irritant, evolve to being corrosive (ants have acid for example), and if the corrosive is oxidative that is short path to making things burn. It would likely be a mixture of several oxidizers and matching stabilizers. Oxidizers would probably mostly be based on oxygen from the air. Chlorine might be easy enough to get near the ocean. Fluorine would be kind of neat to add, but I am not sure if there is a convenient source.

As a practical matter the stabilizers would probably be something that is rapidly vaporized. Inside the dragon it would be continuosly replenished, but as soon as the "fire-breathing" started the chemical balance would break almost instantly.

Some fuel beyond the methane from breathing would probably be also mixed in. Some mixture of alcohols and fat, I'd guess. To give pleasant clinging effect when breathing on someone. And give a higher temperature to get fires started. And cause serious burns even if the target doesn't ignite. Although a strong oxidizer would make most organic things burn well enough.

The probable evolution path would be from a spitting venom, initially targeted at eyes. Then mating rituals. So it would be flashy and mostly cause damage to exposed parts. On targets of reasonable size. If the dragon is much larger than the target, as implied by the question, it would be a lethal weapon.

In the real world the above would kind of imply evolution from snakes as most likely option. I'd actually go with that as snakes re-evolving legs would neatly sidestep issues with six being a wrong number of limbs and allow 2 wings plus 4 legs or 6 legs configurations.

The big issue with dragons, especially when combined with flying, is obviously the size. Realistically the issue has been solved by engineers with either high-energy power generation (airplanes and helicopters) or by making the aircraft float in the air with lifting gas. Since the physical problem to solve is the same these would be the solutions available to draconic (non-magical) evolution as well.

I find the concept of fire-breathing animals, probably commonly fighting each other, being filled with hydrogen less than convincing. Helium would work, but the only sources for it would be ingesting large amounts of methane (methanovore?) or radioactive generation. Tapping underground methane would actually be kind of interesting, as it would explain why dragons spend centuries in underground caverns doing nothing visible to humans. They are breating in the methane, living from the energy of it and harvesting mixed in helium. Actually eating methane might be a draconic attribute even if you skip dragon-blimps. Apart from matching the iconic behaviour of dracons, a source of methane is useful to fire-breathing.

Third lifting gas option would be hot gas, either plain air or steam. This might actually work for a VERY large animal. And needing to generate high temperatures would match with evolving other pyrotechnics.

Problem is that dragon-blimps don't really look very dragonic. So I think I'd skip this option and focus on increasing power density.

I think the easiest way to up power density would be to increase the number of hearts. Basically biological power density is limited by the ability to remove heat and metabolites from tissue. You also need to bring energy in, but that is not generally the issue when talking about power density. This kind of implies that dragons would be able to boost their metabolic rate to level insane. Which would imply very high blood pressure at muscular system, while other parts, such as brain, maintain normal pressures. And one heart maintaining high pressure at a very large animal wouldn't really work that well anyway. Separate secondary circulation systems that boost pressure selectively might work.

By itself this wouldn't be enough, but if you can increase blood pressure, and maybe even have an entirely separate circulation of "something else" with higher power density, you can also replace muscle cells with something else. You can't really make cells work with power beyond certain level, but cells could generate structures capable of higher power in a manner similar to how hair is created. I have no idea how high this could get the power density, but high enough that power density wouldn't be the biggest issue...

So you end up with the structural strenght being the big issue. Hollow or otherwise low density bones are pretty much compulsory. Even then you'd probably need "biologically generated but not living" structures such as I used to dodge the power density issue. Nature has some remarkably strong protein based fibers and glues, so composite structure of fibers combined with strong adhesive seems likely. Something similar to what trees use with cellulose and lignine? Trees can grow to large sizes and protein based solution would plausibly be stronger. Supplemented with similarly reinforced "semi-exoskeleton" of powerful natural armor (very dragonic) and the high density muscles discussed before, this might be enough. Certainly you could get something larger than any living dinosaurs.

Breathing enough oxygen would still be an issue. Dinosaurs and birds have more efficient lungs than mammals do but still. If we assume that the fire comes from a powerful oxidant, the dragon might be capable of storing large amounts of the oxidant and use that oxygen to power up. Or possibly the "new muscles" required anyway, don't consume oxygen directly but work more like a plug-in hybrid does. Dragon sleeps and charges the batteries for the muscles and then the muscles can do a specific amount work without extra metabolism needed beyond the secondary circulation for cooling and energy.

I can see how the exotic bones and hide would evolve naturally as sizes go up. Reinforced structure is useful in intermediate forms and based on natural proteins. Same with extra hearts. Extra control of blood pressure in extremities is useful in intermediate forms for large animals. Evolution for exotic muscles is harder... Then again if we assume a snake re-evolved limbs and already assume an unusual configuration, the exotic muscles might not be evolved from normal muscle to begin with. Which doesn't really suggest how they evolved, but opens up the possibilities enough for the lack of explanation to be less bothersome.

Sorry, for rambling, but this is actually something I have though occasionally about...