If your Fire TV Stick remote won't pair, one of the first things you should do to fix it is reset it: disconnect the Fire TV Stick from the power, press and hold the Left, Menu, and Back buttons on the remote at the same time for 12 seconds. After waiting 60 seconds, put the batteries back in the remote, reconnect the Fire TV Stick to the power, and press and hold the Home button for 10 seconds to start the pairing again.
In case it still doesn't work, make sure that no physical barriers are present and try using the Fire TV app on your smartphone as a remote for the time being to go to Settings > Controllers & Bluetooth Devices and manually add the remote.