Ok there are bad news. Your theory makes a lot of sense when we just evaluate input and output of a dragons den. The problem is that gold is atomically more stable (Au: B/A=7.936 MeV) than carbon (C: B/A=7.468 MeV). That means that you have to explain a huge amount of energy this process consumes. This is alongside the energy that the dragon uses to live and even wastes in the whole fire spitting situation.
Ok there are bad news. Your theory makes a lot of sense when we just evaluate input and output of a dragons den. The problem is that gold is atomically more stable (Au: B/A=7.936 MeV) than carbon (C: B/A=7.468 MeV). That means that you have to explain a huge amount of energy this process consumes. This is alongside the energy that the dragon uses to live and even wastes in the whole fire spitting situation.