How do I open an external url in flutter web in new tab or in same tab

One simple way is to just create a button and use dart:html's window.open() method:

import 'dart:html' as html;

// ...

html.window.open('https://stackoverflow.com/questions/ask', 'new tab');

The name parameter — which I left as 'new tab' — refers to the new tab's window name, about which you can learn more from MDN's documentation.

I think you want this — dart:js enables interoperability between Dart and JS —:

import 'dart:js' as js;

// ...

FlatButton(
  child: Text('Button'),
  onPressed: () {
    js.context.callMethod('open', ['https://stackoverflow.com/questions/ask']);
  },
)