How much should rating fluctuate.

I have an account on multiple sites, I play most of my rated games elsewhere where my rating is around 1450-1520. Is it normal to have your rating change 70 points back and forth?

Absolutely. Your rating is just an estimate of your strength. The system used here, the Glicko system, tells us how accurate it thinks your current 1365 blitz rating is. Right now, it says your "real" blitz rating is likely within 88 points, in either direction, of your current rating- somewhere between 1277 and 1453.  

So 70 points in either direction is completely normal.

(The estimated range is computed based on a statistical model that looks at how often you play and how much your wins and losses follow expected patterns.  A rating deviation (or "RD") score is computed for everyone.  Yours is now 44, which is pretty low. The lower the RD number, the more accurate your rating is considered. New players might have an RD of 200. See  https://www.chess.com/article/view/chess-ratings---how-they-work  )

And there is no connection between the two sites, so a wide fluctuation between ratings on the two sites is normal.

thanks so much! very informative answer.