Flame Goldens, (Chrysolophus pictus pictus infuscatus) are not a new mutation. Although they look like they are similar there are slight differences if you look closely.
Chrysolophus pictus pictus obsurus
has more phenotypic resemblances to Chrysolophus amherstiae, such as barring in the tail feathers, the dark ash throat and sometimes the green neck/breast feathers of Chrysolophus amherstiae are present in the Dark Throated Goldens, not quite green and not all red but a mixture of the hues and has the lacing of the feathers of Lady Amherst, leading to the thinking it has under gone selective breeding, instead of a actual mutation.
Chrysolophus pictus pictus infuscatus or 'Flame Golden' and sometimes know as 'Salmon Golden' too! Is thought to be a true mutation of Chrysolophus pictus but the Dark Throated was also thought to be an original mutation, it has since it's discovery in 1860 been now thought to be a result of selective breeding, rather than a mutation.
Little scientific data supports these theories but unlike the Flame Golden, Dark Throated have 26 bp cytochrome gene changes between them and the true Golden pheasant, of which it was previously thought to have mutated from....not likely this could occur in just 137 years. It is also autosomal incomplete dominate.
The Flame Golden has no such gene changes and this is why it is thought to be a natural mutation. This may change as more scientific studies are done but for now this is the common thought process.