The Fire TV platform does not use Automated Content Recognition to identify the shows you are watching, but does collect data about what you are watching using an antenna and using some streaming apps, depending on your privacy settings.

Fire TV privacy settings are available on the TV in Settings > Privacy Settings. On older devices, the settings may be in the Applications menu.

• Device Usage Data includes information about how you use the device, and is used for advertising and marketing.
• Collect App and Over-the-Air Usage Data includes data about what you watch using an antenna, and which smart TV apps you use.
• Interest-Based Ads controls whether Amazon shows you ads based on what it infers your interests to be.
• Manage Sharing From Apps controls whether third-party apps send viewing data to Amazon.

Source: Consumer Reports