Use the chrome.devtools.network API to retrieve the information about network requests displayed by the Developer Tools in the Network panel.

class ChromeDevtoolsNetwork extends ChromeApi {
 static final JsObject _devtools_network = chrome['devtools']['network'];

 ChromeDevtoolsNetwork._();

 bool get available => _devtools_network != null;

 /**
  * Returns HAR log that contains all known network requests.
  * 
  * Returns:
  * A HAR log. See HAR specification for details.
  */
 Future<Map<String, dynamic>> getHAR() {
   if (_devtools_network == null) _throwNotAvailable();

   var completer = new ChromeCompleter<Map<String, dynamic>>.oneArg(mapify);
   _devtools_network.callMethod('getHAR', [completer.callback]);
   return completer.future;
 }

 /**
  * Fired when a network request is finished and all request data are
  * available.
  */
 Stream<Request> get onRequestFinished => _onRequestFinished.stream;

 final ChromeStreamController<Request> _onRequestFinished =
     new ChromeStreamController<Request>.oneArg(_devtools_network, 'onRequestFinished', _createRequest);

 /**
  * Fired when the inspected window navigates to a new page.
  */
 Stream<String> get onNavigated => _onNavigated.stream;

 final ChromeStreamController<String> _onNavigated =
     new ChromeStreamController<String>.oneArg(_devtools_network, 'onNavigated', selfConverter);

 void _throwNotAvailable() {
   throw new UnsupportedError("'chrome.devtools.network' is not available");
 }
}