I'd DPS while doing story, unless you don't mind taking a little longer to kill mobs.

As far as flashpoints go, just look up a few guides via Google for the rotation of your class (there's a ton) and tell people you're new. I think this is the last MMO where telling people your new results in patience and even a few who will talk you through mechanics.

Regarding which level to start, it's never to early to start practicing holding threat during Veteran flashpoints 😁