You might be able to get more feedback posting your question at the Amazon Fire TV Stick help forum. FireOS is based on Android but it's still a matter where you're only going to interact with the FireOS interface, not Android that's running beneath.
https://www.amazonforum.com/s/fire-tv
It might also help if you're more forthcoming with what might be relevant details
-- What kind of TV do you have? Presumably it's a SmartTV but since you're using Fire TV Stick is it an older TV that just has HDMI? What make and model TV?
-- What mobile device are you using? Tablet or Phone? Which model and which version of Android is it running? Or are you using an iPhone?
-- Since WiFi isn't an option instead of mobile device-to-Fire TV Stick-to-TV have you tried using USB to HDMI cable? (wired vs wireless)