The Pokemon species depends on the Female you breed. So you want a baby Vulpix ergo you will need a Female Ninetales.
The moves the baby has are passed down by the Male.
Vulpix cannot learn Fire Blast as an egg move unfortunately. These are the moves it Can learn
I'm not sure what egg moves are best, but they have to be known by Arcanine.
This link and the first answer by PlumpyFoof explains the Father/Egg moves quite nicely.