I have an arcanine with 77% iv and the attacks fire fang and flamethrower. Should i keep it and power up?

I suggest to just keep it, but not recommend to power up. If you power up, it waste your stardust and candies if you have a better one in some day. The reason I suggest to keep it is gym battle.

Your Arcanine's moveset is the best moveset for defense, and the third best moveset for offense. The problem is, that even though you have the best defense moveset, Arcanine is not a great defender because of its typing. In the current meta Fire is probably the worst typing for defense because of the overwhelming amount of Vaporeons people have to attack. So even a really bad Vaporeon can easily destroy Arcanine. Every attacker probably has several Vaporeons available for attack so as of now Arcanine's best job is just to use it to attack Grass and Ice Pokémon.

Then again for attacking, your Arcanine's moveset is almost 7% worse than the optimal one (Fire Fang/ Fire Blast). Given that your Arcanine doesn't have exceptional IV's either (don't get me wrong, it's definitely decent) I would probably not use candy to power it up, unless you have tons of excess stardust, people don't have many Vaporeons in your town or you are lacking anything better to attack Lapras.

TL;DR: My advice is, keep it, but don't power it up, you won't lose anything even if you later decide to power it up. There's no hurry to power up anything until you're level 30 (cap for wild Pokémon).

I would keep it, but not power it up. Just throw it in some gym where you think no one will contest and leave it there.