I currently have a shared library of shows on my NAS device and all four of my devices (2 Nexus Players and 2 FireTV) point to that library. All is working fine but the question I have is when I watch a show how can I get it to be checked off as watched on all devices?
Check your NAS user manual (or settings interface). A lot of them have MySQL server capability, or a way to add it.
Or buy a raspberry pi2 or other cheap arm box and run mysql on it.
Your NAS does seem to able to run a MySQL server, according to
Installing MySQL on Buffalo NAS but it doesn't seem as convenient as on some other NASses like Synology. At least it is possible.