To install the Kodi app on your Amazon firestick, you will need to know how to install app from unknow source on your firestick, if you dont know how, you may read about it in one of my post by clicking the above link.
I will assume you have gone through the above link.
To install Kodi app now follow the steps below.
1. On the home of your firestick, click on the app list at the top right close to the settings icons. Once this opens, scroll down to locate the DOWNLOADER APP you installed from the install app from unknown source post. Open the Downloader app, note that a couple of prompts will be displayed when you run the app for the first time. You should finally be on this home screen of the Downloader app (Home tab in the left menu is selected). On the right part of the Downloader app home screen, select the text box.
2. Enter the following path/URL in this textbox using the onscreen keypad: firesticktricks.com/kapk
3. The APK file of the Kodi app will now download on your device. It won’t take too long; it is a small file.
4. When the APK file has downloaded, the installation prompt is displayed. Click Install. After that, give it a minute and you will now see the installation progress on the screen.
As soon as the Kodi app is installed, the following message is displayed. Now you are free to click OPEN and start using the app. You will have to click DONE (recommended). This will allow you to go back to the Downloader app and delete the Kodi APK you just downloaded. The reason for this is to saves space on limited FireStick storage.
5. On this prompt, click Delete.
6. Choose Delete again.
Thats all, let me know if you have any trouble with it.