Answer for Kodi Upgrade on Fire TV stick

It sounds like you already found my tutorial on How to Install Kodi on Amazon Fire TV Stick
 
You can simply follow those instructions again to install the latest version and it will essentially “update” it to that version. All your settings remain intact, except for some rare cases where an addon you had is not compatible with the latest version. 
 
I haven’t had any issues like that, and I do much prefer that latest Kodi 17 over 16.  The new default theme, Estuary, is pretty nice.