1. Enabling ADB debugging and apps for unknown sources
Turn on your Firestick and scroll down to 'Settings' click it and then navigate to 'System', once on system click it and scroll down to 'Developer options'. You will see 2 options, turn them both to 'ON'.
Settings > System > Developer options > Switch both to 'ON'
Doing this allows for applications outside of Amazon to be installed, in this case Kodi.
2. Installing ES File Explorer (This is needed to install Kodi)
Press the Home button and Navigate to 'Search', Click it and type in 'ES File Explorer' and select the first option, make sure to type it in exactly as I have written it. It will then search for the app. Click on the first app and press the Download' button.
Search > Type in 'ES File Explorer' > Click the text below > Select the first app > Press 'Download'
Installing ES file explorer will allow for the installation of Kodi, which I will show you in the next step.
3. Navigating to the Kodi download website
Open up ES file explorer and go to the favorites option, then scroll down to 'Add'. In 'Path' type in 'http://kodi.tv/download, in 'Name' type in 'Kodi' and then press 'Add'.
Favorites > Add > In 'Path' type in 'http://kodi.tv/download > in 'Name' type in 'Kodi' > Press 'Add'
Once this is done goto 'favorites' and scroll down until you see 'Kodi', click 'Kodi.
Favorites > Kodi > Click Kodi
Following these steps should have taken you to the Kodi download site.
4. Downloading and installing Kodi
Once you are on the Kodi download website you have to scroll down until you see 'Android' and select the 'ARM option' under the Android logo. Make sure to install the latest non beta version for everything to work properly.
Navigate to Android > Click ARM
Sometimes the ARM link will do nothing when you click, to fix this just keep pressing it and holding down for a few seconds and letting go, it will work you just have to be patient.
4.1Now a box will come up saying open folder or file, Open the file. This should start the download of Kodi. Let this complete.
Click open file
4.2Once the download completes you will be given 3 options, select install.
Once you press install Kodi will be added to your Amazon Firestick.
4.3You can find kodi under settings and then navigating to applications and then scolling down to 'Manage installed applications' and then find Kodi.
Settings > Applications > Manage installed applications > Kodi