No. You should be using your TM on meta relevant pokemon. Or at least on pokemon that are useful, arcanine is not the case.
If you're a new player you should focus on building a decent team. Check tier lists on this site to find out what you will be needing.
If you are a veteran player who has 30+ cTM and just wanted to use them because they take space, then go ahead and TM your arcanine.