When using the Amazon FireTV, either a WiFi or wired Ethernet connection are supported. However, when using the wired Ethernet, after selecting an external server in MCPE, the following error is presented:
Unable to connect to the world. Please check your connection to the Internet and try again.
The device does have an Internet connection and MCPE does detect connectivity to the server (it is listed with a green dot in the "Play" screen). All streaming content and other games I have tried work fine.
Note: as a developer myself recently porting an Android game to the FireTV, I found that I too was not checking for the Ethernet port as a valid connection type; I had to explicitly check the connectivity manager for connection types "WIFI", "MOBILE", and "ETHERNET" before deciding there was no connection available.