I am trying to install this printer, but can't seem to find a driver that works. Brother does have Linux drivers, but being new to BSD I don't know how you would install them. I'm thinking they should work since both BSD and Linux use CUPS, but I'm not sure how to access them on my new system.

First I would recommend you to install gnome-cups-manager.
I didn't find any of the PPD file for that printer my self.