To download the app from the Kodi developers, we'll use another app called Downloader. This application can be found by searching for Downloader in the Appstore.
Download and install the app.
We'll need to enable apps from unknown sources. This tells the Firestick that it's okay to install third-party apps.
Open Settings and choose My Fire TV (older models will say Device instead).
Under Developer Options, select Install unknown apps (older models will say Apps from Unknown Sources instead)..
Then, select Downloader to toggle the setting to ON.
Using your Fire Stick remote, navigate to the Downloader app and launch it.
The first time you open Downloader, it will prompt you to allow it to access photos, media, and files on your device. Select Allow.
Next, open Browser from the left-hand navigation menu. Enter the following address:
Scroll down and select Android from the list. You can choose to download the 64bit or 32bit version. Feel free to experiment with both to see which works best for you. I'm installing the 32bit version.
Once your download has finished you will be prompted to install the package. Click INSTALL.
You can now open Kodi from your main menu. It will be listed among your current selection of apps. When you access Kodi for the first time, it will prompt you for permission to access media files and folders. Be sure to give it the permissions it needs.
Now it's time to add some media! Visit the official Kodi wiki for help adding your own videos, music, and more. This Video library page is an excellent starting point for understanding the Kodi menus and how to add your own media library.
Updating Kodi on the Firestick is easy.
Remove the current version by going to Settings > Applications > Manage Installed Applications.
Select Kodi from the list. Choose Force stop then Uninstall.
Open the Downloader app and navigate to the Kodi downloader URL:
Select the latest Android version to download and follow the installation prompts. Congratulations! Your Firestick now has the latest version of Kodi.