Can access Apple TV from Firestick but Showtime not available. Why not?

Showtime would be available as an in-app Channel to the Apple TV app for the US region. But Fire TV users unfortunately can’t subscribe or make purchases for Apple services on that device. They will have to do so on a different device.

You can get Showtime as a separate app directly on your Fire TV streaming device from the Apps and Games Store. That wouldn’t be related to subscriptions through Apple.