Diagnosis
The remote has lost its Bluetooth pairing with the TV. The blinking orange light is it searching for a connection. This can happen after a TV software update or if the batteries were removed for a while.
How to Fix It
Hold the Home button on the remote for 10 seconds. This forces it back into pairing mode. On the TV screen, a prompt should appear to pair the remote. If it doesn't, go to the TV's Settings > Controllers & Bluetooth Devices > Amazon Fire TV Remotes > Add New Remote and follow the prompts while holding the Home button.
If That Didn't Work
Try fresh batteries first. If the remote still won't pair, you can use the Fire TV app on your phone as a temporary remote to navigate the TV menus and attempt the pairing process from there.
Heads Up
The remote uses Bluetooth, not infrared. That's why pointing it at the TV isn't necessary for pairing, but also why it won't work at all until paired.