How exactly can I justify fire breathing animals? I mean, how would they do it in a scientifically and physically possible way?
Why not look at the bombardier beetle for inspiration?
Basically, two glands with chemicals which react when they are mixed. So the creature takes a deep breath, opens its mouth and blows while spraying the chemicals from the glands. The chemicals mix and ignite, meaning that you don't need to have a spark to get fire.
Snakes have glands that contain poison, and some snakes are able to spit. Mix in the biology of the bombardier beetle, and a creature that has glands that contain chemicals that react by igniting and can spit/spray the chemical mixture is biologically and scientifically possible.
Basically - yes. We know that there are bacteria and digestive processes that produce methane, a flammable gas, and a dragon with these bacteria inside of it could, in theory, produce high levels of methane. We know that there are organisms which have bladders to store things like venom, ink, and other defensive fluids. The only thing that would be needed would be a way to produce enough heat. I think that the model of an electric eel could work here - if the dragon were able to build up enough electric energy for a sizable spark inside of its mouth (maybe from one side to the other?), it could ignite the methane as it passed through and was expelled.
This idea was explored in-depth in a movie called Dragons: A Fantasy Made Real. They theorized that dragons might produce a flaming breath by utilizing the natural reaction of bacteria in the gut that produced hydrogen as a byproduct. The hydrogen would be funneled into a bladder that doubled as a flight assist. These dragons would eat from platinum or palladium veins. Since platinum and palladium both cause combustion when exposed to hydrogen, exhaling hydrogen from the bladder would produce a flaming breath for as long as the creature had hydrogen stores, provided it still had any mineral dust in its mouth.
Look at bombardier beetles... they secret hot chemicals as a defense mechanism. this is close to fire breathing, i think.
I think there would have to be a gland of some sort which you can make up that contains a combustible secretion. Further more I think that dragons would have to take a note from birds. Some birds swallow rocks to help them digest. In this case the rocks would be used to create a spark. I believe the gland that birds have is called a gizzard.