I think it is biologically possible for a fire breathing creature to exist. This is how it can work: The creature has a special gland that secretes a highly combustible substance that ignites only when exposed to air in the form of a fine mist. So when the creature gets afraid the glands secrete lots of the substance and the creature exhales it violently in a fine spray that ignites outside the creature's body but does not burn the creature.
Alternatively, it could be two different glands that produce two different substances that ignite when mixed together in air. The creature sprays two jets of the substance that converge at a safe distance outside the creature's body.
The creature uses this as a defense mechanism protect its helpless young. It seems impossible for an animal to be able to breathe fire but I think chemistry makes it possible.