Creating a Flutter app that blocks access to specific websites across the entire device is technically possible but requires advanced integration with the underlying operating system. However, such functionality usually involves significant limitations and permissions due to security and privacy concerns on modern operating systems.

Here’s how it might be approached:

1. Using a VPN Service flutter_vpn

2. Using a Proxy Server Another approach is to set up a proxy server that filters network traffic and blocks requests to specific domains. The app configures the device to use this proxy.