You're better running off a Physical Attacking Arcanine rather than a Special Attacking or Mixed. While the recoil is annoying, there really isn't any better option as a Special Attacking Arcanine lacks in coverage and in moves in general, especially since Reborn already is lacking in TMs and Move Tutors.
As long as you have Flare Blitz and Extreme Speed for Priority, you can pretty much run whatever you choose to from moves like: Close Combat, Crunch, Outrage, Iron Tail, Bulldoze, etc.
EDIT: Just remembered Mixed Arcanine is actually decent. You can try that if you really don't want to deal with recoil from Flare Blitz, but I wouldn't do it personally.