Buy the KODI app at amazon website. It's free!
1. Go to Amazon website and log in using the account that links to all of your amazon devices
2. Search for kodi and make a free purchase of this app. Done!

Launch KODI app from your device
1. Do a normal launch by selecting settings -> application -> managed all application -> kodi
2. Exit KODI or press home button on the remote.

Now you should see the kodi icon under Home -> Recent. Normal behavior like other apps