I have two users setup. When I open the Fire TV app, I am given the choice of manually entering a user or picking a server. Just to be sure, I picked my Jellyfin server, which shows up just fine. Still no users. I manually enter a user and password and voila…Jellyfin UI.
Users are hidden by default on the login screen. There’s an option in the users settings to hide the users, if you want them to appear you can untick this. You go to Server Dashboard->Users->Select User. At the bottom of this screen you’ll find “Hide this user from login screens” untick this, hit save and that user should now show up on the app logins screen. Repeat for all users you want to appear