This is easy!
1. From the Fire TV device’s home screen, scroll to “Settings”.
2. Next, scroll to the right and select “Device”.
3. Next, select “About”.
4. Next, scroll down to “Network”. Your Fire TV device’s MAC Address will be listed on the bottom right as a set of 12 numbers and letters in pairs, separated by colons. When entering this MAC into your allowed devices list, include all characters with the colons for the method that you are going to connect it with (ie, if you're connecting via WiFi, use the WiFi MAC address)