I finished the Dawnguard side of the quest, and now I'm wondering if I can still get the vampire power rings and amulets. Is that possible?
No. You can't get the quest to find the rings until you finish The Bloodstone Chalice; if you sided with the Dawnguard instead of taking Harkon's gift, you don't get The Bloodstone Chalice quest. The rings spawn semi-randomly when you accept the quest, so they won't be in the world for you to otherwise find.
The same is true of the quest to get the amulets.
Besides, the gentleman who gives you the quest will either be inaccessible (as the castle got locked behind you), dead (if you killed him later) or at least hostile towards you.
The rings are
xx00e7fd (see here for the meaning of
xx) if you want to cheat yourself a pair though. The amulets are