Once you have finished the Campaign, you can continue to play onward and the Flashpoints (if you have the Expansions) will begin to spawn in.
IMO if you're interested...
Me personally, I would prefer to start a new Career mode game if you have Expansions installed. This is because the Flashpoints are rated anywhere from 1.5 skulls to 5 skulls. If you play the Flashpoints after the Campaign, you most likely have an Assault lance and many Flashpoints will be too easy. I myself like playing from scratch and taking Flashpoints as my Career company grows.
This is of course just preference, but I feel like you would get more from playing a new Career and playing Flashpoints from there. Also, Career Mode has a scoring system over 1200 days (does continue past 1200 days), so if you like playing for a rank, that is another good reason to play a Career game.