Ah, but who is to say that the Vulpix and Ninetales that we all know is the way they originally looked either? Perhaps they were once normal type pokemon and over time they began to develop into different forms with different types. That way while the fire Vulpix we all know became the dominant form elsewhere, the ice type developed independently from the original pokemon in Alola? That's how actual evolution works - the ice Vulpix would not be descended from the fire Vulpix, but would be a sister species.
If you look at the tigers that are alive today, three examples are the Bengal Tiger, which is pretty large and adapted to temperate and tropical forests of India, the Siberian Tiger is larger still and has longer fur, making it adapted to the cold weather of Siberia, while the Sumatran tiger is the smallest one, an adaptation to living on an island. But none of these animals are descended from the other - they all have a common ancestor that lived in all three places and slowly adapted to better suit those places.
For this reason, there may be no reason for the Ice Vulpix to have access to Flamethrower, unless, as you say, it is done through breeding. But then again, look at Eevee. Glaceon doesn't get Flamethrower, even if its raised by an Eevee hatched from an egg produced by a Flareon.