I have used my Firestick in France and SXM but the last time was a year ago. I remember seeing "We've noticed you are in a different country and some programs will not be available" on the TV BUT I was able to watch what I wanted. Another method i use is just cast from my laptop to the tv using Chrome and the Stick or a Chromecast dongle. Netflix can also be used this way.
I'm sure you already saw this but the FAQ is a bit confusing and combines Amazon Video (rentals) and Prime TV (regular shows) and involves changing your country of origin in settings...a bit involved.
https://www.amazon.com/gp/help/customer/display.html?nodeId=201624360I have two sticks..one for travel and one stays connected at home.