adbLink can manage Kodi via USB as well as via Ethernet/WIFI. USB Mode is available for both Fire TV and Fire TV Stick.
To detect USB-connected devices the Fire TV's Settings-System->Developer Options/USB Debugging must be enabled and the device connected via USB Cable to your PC.
Please note that some USB cables are for charging only, not for data I/O. Unfortunately, there is no way to visually detect a charging-only cable. It just won't work.
You may have to wait a few moments for adb to detect the device. You may have to stop the ADB server then press refresh several times; the Stick especially can be stubborn.
Once detected you will see a USB serial number appear in the connected devices listbox.
Once connected via USB, double-click the USB serial number to bring up an empty device record with the USB serial address already filled in. Complete and save the record and you will be ready to manage this device via USB.
In rare cases you may find it easier to use adbLink's console to establish a USB connection. If so, once you are connected just refresh the connected devices listbox to add the device's USB serial number.