This tutorial will help you install Kodi on your FireTV stick using any android device via sideloading or FTP. All you need is a WiFi connection to be able to transfer files from your Android device to your FireTV Stick.
Apps for download:
Apps2Fire : https://play.google.com/store/apps/details?id=mobi.koni.appstofiretv&hl=en
Kodi app (ARM Version): http://mirrors.kodi.tv/releases/android/arm/kodi-16.1-Jarvis-armeabi-v7a.apk