This is a super old post I know; but is this possibly a case of determining who is a true, worthy Targaryen and who isn't? Brightflame was a cruel mad man and not in any way fit to rule or hold power. Rhaenys might be seen the same - she lost the dance and burned for it. Viserys is the same.
Maybe having some kind of fire proof power is a testament to just how Targaryen/worthy of the throne you are.