No you cannot run a Flutter Web application in the mobile browser locally, if you want to test your application with a mobile format you can simulate it from a Google Chrome browser by enabling device toolbar from the developer tools Ctrl+Shift+M .
Read moreCan Flutter app run on web?
The web itself is a flexible platform, but Flutter is ideal for building web applications like PWAs or SPAs and bringing your existing mobile app to the web .
Read moreHow do you create a Flutter on the web app?
Building a web application with Flutter
Read moreCan we build Flutter app online?
Build the app for deployment using the flutter build web command . You can also choose which renderer to use by using the –web-renderer option (See Web renderers).
Read moreHow do you run the Flutter app online?
Tools support for Flutter web development
Read more