Yes, just download the FITE Fire TV app and sign in with your FITE account. This will sync your purchase if you've made one. You can also buy Triller Fight Club: Holyfield vs Belfort directly from the Fire TV app itself.
Important: At this point in time Facebook log in cannot be used on Fire TV. You have to reset your password from https://www.fite.tv/account/login/ and enter your Facebook email. Use the new password to sign in.