Display contacts birthdays on stock Samsung calendar app
You probably figured it out by now, but the calendar of birthdays only syncs with the Samsung account. 

The fastest way to link a different account to the Samsung account I could find without re adding contacts was by adding a relationship to the contacts you want to set up.

I did this by going to my  Contacts app, clicking on my own profile, and under the relationships section adding a relationship. I did it with my family members and they started showing up right away.