I installed KODI on my 4K Fire Stick a few days ago.
There's no way to attach a USB stick so you would need some sort of SERVER device (on the same wi-fi network) like my WD MY CLOUD. I had to add the source within KODI and in my case the option that worked was through "NFS..." not SMB or whatever other options where there... I then found the "MOVIES" folder, added it, then said to use the Movie Database as the reference to add thumbnails etc.
That's the only way to do it. If you have no compatible server device you can't add content.