If you are on a BlackBerry device running BlackBerry OS 10.3.1 and install the Fitbit app from Amazon, they will sync. I was able to sync before on OS 10.3 but it was a bit finnicky, now my BlackBerry Passport syncs to my Fitbit automatically. I even get a notification of incoming calls on my Fitbit Charge but it does not display the caller's number.
There is a member named Lopellen who posted a BlackBerry app feature request in this forum. Please add your vote and comments. You might also want to contact Fitbit's customer service directly to let them know what you want. The more they hear from people, the more they will realize that there's a growing number of BlackBerry users out there who want a native BlackBerry 10 app.