Not using a Fire TV Stick, I can’t speak from personal experience. So I’m unsure if and how a Fire TV Stick would integrate with Avast.
It’s strange that you aren’t getting any error message from Avast.
So I did some searching and some are saying you can’t unless you have installed the Avast VPN on the fire tv stick:
This was one of the hits, but the Avast VPN is a paid product.