Amazon sells two devices that both look like candidates for digital signage, and they are set up in completely different ways.
Fire TV
A television accessory. Screenly installs on it as an app from the Amazon Appstore. Fire OS is built on Android, so it behaves like an Android device once Screenly is running on it.
Amazon Signage Stick
Purpose-built signage hardware. There is no app to install. You pair it through Amazon’s own Signage console, choosing Screenly as the CMS provider. See Amazon Signage Stick.
Note
If you are buying hardware for a new screen, the Signage Stick needs no sleep or screensaver settings changed. A Fire TV does.