Here are the steps that you should follow while setting up Kodi on Amazon Fire TV Stick and you also use Amazon Fire Tv Support in case you need any guidance in setting up Kodi.
Go to the Settings of Amazon Fire TV Stick > Developer > turn off Apps from unknown sources.
Use ES File Explorer as a file management program.
Now Search ES File Explorer in App Store, download it, and for adding it go to the left of the application.
Then there will be a box for filling some information.
In Path text box, you will have to write the following download address for Kodi http://kodi.tv/download . Then you can this link to your favorites list.
Tap the ARM link. Nothing will happen after tapping but don’t worry it is natural.
Go to the 3 dots in right-hand corner in the bottom, tap on it, and select the option of Open in new Browser.
Now Kodi will download. After downloading it will ask for your permission for installation.
You are done now. Kodi has been installed.