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 Jake Paul vs Gib/Andrade vs Keeler 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.