Extremespeed and Flare Blitz are a must for Arcanine. Thunder Fang is also a good move to have around and deal with Water and Flying types. Hidden Power Grass is a good option for the fourth moveslot, since it provides type coverage and works off of Arcanine's good Special Attack. However, you could also use Hidden Power Ground to take down Fire types, but HP Grass is usually better. However, there are some other good options for the fourth moveslot:
Toxic: Takes down foes who would otherwise be unaffected by Arcanine's other moves.
Will-o-wisp: Helps take down Physical sweepers.
Iron Tail: To deal with Rock types.
Dragon Pulse: To deal with Dragon types.
Overall, the best moveset would probably be: Flare Blitz, Extremespeed, Thunder Fang, HP Grass/Iron Tail