Personally, I'm getting increasingly annoyed with my Fire Stick. It's kind of sluggish, and very locked-down. You used to be able to sideload a custom home launcher, but Amazon is cracking down on that. Their launcher is filled with bloat and ads. Recently I've noticed mine auto-playing Amazon Prime video trailers on boot which makes me want to throw it out the window.
I have JF installed on my Samsung (Tizen) TV and it works great. And the TV will auto-launch back into JF on boot... something I wish Fire Stick allowed.
PSA: Pre-built images are available, which avoids having to compile the app yourself. https://github.com/jeppevinkel/jellyfin-tizen-builds
The install process is pretty straightforward. I'd recommend giving it a try. More or less copying commands, then you're left with the Jellyfin client on the TV. Works great once installed.
No Kodi sadly though.