Hello FaridDAR,
Welcome to Apple Support Communities. Having green flashes while watching Apple TV will definitely keep you from enjoying your shows, and we'd be happy to look into this with you.
Let's try starting in safe mode. Does the issue still persist in safe mode? If so, restart your Mac after doing so, and keep us updated.
Here's how to start up in safe mode:
How to use safe mode on your Mac
Also, let's go ahead and test this out in a test user account on your Mac. This will help us narrow things down to see if it's potentially an issue within your user account or not. This article shows how to do that:
Set up users, guests, and groups on Mac
We hope this information is useful. Kind regards.