You can achieve that using flutter_web_browser plugin which opens web page in-app in Android chrome tabs style.
Ex:
body: new Center(
child: new RaisedButton(
onPressed: () => openBrowserTab(),
child: new Text('Open website'),
),
),
openBrowserTab() async {
await FlutterWebBrowser.openWebPage(url: "https://gadgets.ndtv.com/", androidToolbarColor: Colors.deepPurple);
}
Result:
Hope this helps.