Yes it is legal. However, as far as I can tell, it is only possible using Smeargle. This is because nothing else in Arcanine's Egg Group can get both Double-Edge and Close Combat on the same move set.
If you prefer one over the other, then your options for the father are:
Close Combat: Monferno, Infernape, Lucario, Mankey, Primeape, Smeargle, and Zangoose
Double-Edge: Spinda, Skitty, Rattata, Raticate, Cyndaquil, Quilava, Typhlosion Phanpy, Smeargle, Numel, Camerupt, Hippopotas, Hippowdon, Deerling, and Sawsbuck
As you can see, Smeargle is the only thing on both lists. As for the other two moves, Outrage and Flare Blitz, they are easy enough because Growlithe gets them both levelling up (at levels 43 and 45, respectively), so just wait until after that before evolving it.
Assuming you don't want to bother with Smeargle (if you do, then be my guest), I would suggest taking Close Combat through breeding, and get Crunch (learnt by Growlithe at level 39) instead of Double-Edge, as it would give you more type coverage. In particular it gives you something to use against Ghosts.
I hope this helped.