Should I power up or reroll my Arcanine?

I don't think there is much difference between the two moves. I would hold out for something better.

No Reason to waste TMs, Arcanine ist easy to obtain

Don't waste TM on it since it already have 2 fire moves and I would take a flamethrower over a FB anyway.

Check out this video comparing Arcanine move sets.

https://www.youtube.com/watch?v=LDusWZhgVKo&t=98s

Keep flamethrower, power him up.
In the old gym system flamethrower was often superior to fireblast. FT does 97% of the damage of FB, but in two shots. That meant you often got in an extra half attack with FT before your arcanine fainted. It is also harder to dodge FF then FB.

I've got a Arc on lvl 35,5 with the same moveset as above. Imo flamethrower is superior; putting in an extra bar charge before going out.

I use flareon with fire spin + overheat if I need to put out some large damage input; time limit.