There is no difference for the Stick:
- install a file manager on the stick (ES is available on Amazon app store);
- enable "Install apps from unknown sources";
- open a browser, go to Kodi page, download the APK for FireStick;
- open the file manager, and click on the download, it will install, and Kodi icon will go on the home screen.
This is one of the first link searching for "Kodi for amazon fire stick"
You may want to try first older version like 17.x (it works for sure on my Stick), instead of jumping straight to 18