This gist demonstrates the use of the Flutter Navigation rail widget to implement a responsive side menu. Feel free to improve it.

Navigation Rail Demo Flutter Web

import 'package:flutter/material.dart';

void main() {
  runApp(MyApp());
}

class MyApp extends StatelessWidget {
  // This widget is the root of your application.
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: HomePage(title: 'Events'),
    );
  }
}

class HomePage extends StatefulWidget {
  HomePage({Key key, this.title}) : super(key: key);

  final String title;

  @override
  _HomePageState createState() => _HomePageState();
}

class _HomePageState extends State<HomePage> {
  int _selectedIndex = 0;
  bool _extended = false;

  List<NavigationRailDestination> _buildDestinations() {
    return [
      NavigationRailDestination(
        icon: Icon(
          Icons.drafts_rounded,
          color: Colors.black87,
        ),
        selectedIcon: Icon(
          Icons.drafts_rounded,
          color: Colors.indigoAccent,
        ),
        label: Text('Saved Drafts'),
      ),
      NavigationRailDestination(
        icon: Icon(
          Icons.pending_rounded,
          color: Colors.black87,
        ),
        selectedIcon: Icon(
          Icons.pending_rounded,
          color: Colors.indigoAccent,
        ),
        label: Text('Pending'),
      ),
      NavigationRailDestination(
        icon: Icon(
          Icons.done_rounded,
          color: Colors.black87,
        ),
        selectedIcon: Icon(
          Icons.done_rounded,
          color: Colors.indigoAccent,
        ),
        label: Text('Review'),
      ),
      NavigationRailDestination(
        icon: Icon(
          Icons.done_all_rounded,
          color: Colors.black87,
        ),
        selectedIcon: Icon(
          Icons.done_all_rounded,
          color: Colors.indigoAccent,
        ),
        label: Text('Validated'),
      ),
      NavigationRailDestination(
        icon: Icon(
          Icons.check_circle_rounded,
          color: Colors.black87,
        ),
        selectedIcon: Icon(
          Icons.check_circle_rounded,
          color: Colors.indigoAccent,
        ),
        label: Text('Approved'),
      ),
      NavigationRailDestination(
        icon: Icon(
          Icons.cancel_rounded,
          color: Colors.black87,
        ),
        selectedIcon: Icon(
          Icons.cancel_rounded,
          color: Colors.indigoAccent,
        ),
        label: Text('Rejected'),
      ),
    ];
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
        appBar: AppBar(
          title: Text(widget.title),
        ),
        body: Container(
          width: MediaQuery.of(context).size.width,
          child: Column(
            crossAxisAlignment: CrossAxisAlignment.start,
            mainAxisAlignment: MainAxisAlignment.start,
            children: [
              Expanded(
                child: Row(
                  children: [
                    Expanded(
                      flex:3,
                      child: Row(
                        children: [
                          NavigationRail(
                            selectedLabelTextStyle: TextStyle(
                              color: Colors.indigoAccent,
                              fontSize: 14,
                              letterSpacing: 1,
                              decorationThickness: 2.0,
                            ),
                            unselectedLabelTextStyle: TextStyle(
                              color: Colors.black87,
                              fontSize: 13,
                              letterSpacing: 0.8,
                            ),
                            leading: _extended
                                ? Padding(
                                    padding:
                                        const EdgeInsets.only(left: 16.0, right: 16.0, top: 8.0, bottom: 16.0),
                                    child: FloatingActionButton.extended(
                                      backgroundColor: Colors.indigoAccent,
                                      onPressed: () {},
                                      label: Text('Create Event'),
                                      icon: Icon(Icons.create_new_folder_rounded),
                                    ),
                                  )
                                : IconButton(
                                    icon: Icon(
                                      Icons.create_new_folder_rounded,
                                      color: Colors.indigoAccent,
                                      size: 40,
                                    ),
                                    onPressed: () {}),
                            trailing: Padding(
                              padding: const EdgeInsets.all(16.0),
                              child: Container(
                                  alignment: Alignment.bottomRight,
                                  child: IconButton(
                                    onPressed: () {
                                      setState(() {
                                        _extended = !_extended;
                                      });
                                    },
                                    icon: _extended
                                        ? Icon(
                                            Icons.arrow_back_ios_rounded,
                                            color: Colors.indigoAccent,
                                          )
                                        : Icon(
                                            Icons.arrow_back_ios_rounded,
                                            color: Colors.black87,
                                          ),
                                  )),
                            ),
                            extended: _extended,
                            minExtendedWidth: 200,
                            elevation: 2.0,
                            // backgroundColor: Color.fromRGBO(32, 176, 44, 0.96),
                            labelType: NavigationRailLabelType.none,
                            selectedIndex: _selectedIndex,
                            destinations: _buildDestinations(),
                            onDestinationSelected: (int index) {
                              setState(() {
                                _selectedIndex = index;
                              });
                            },
                          ),
                          VerticalDivider(),
                          Expanded(
                            child: _renderMainContent(_selectedIndex),
                          ),
                        ],
                      ),
                    ),
                    Expanded(flex:1,child: Container(color: Colors.black54,child: Column(children: [
                      Text("Event Detail Overview",style: TextStyle(color: Colors.white),)
                    ],),)),
                  ],
                ),
              ),
            ],
          ),
        ));
  }

  Widget _renderMainContent(int index) {
    switch (index) {
      case 0:
        return Column(
          children: [
            Container(
              child: Text('Saved Drafts'),
            ),
          ],
        );
        break;
      case 1:
        return Column(
          children: [
            Container(
              child: Text('Pending'),
            ),
          ],
        );
        break;
      case 2:
        return Column(
          children: [
            Container(
              child: Text('Review'),
            ),
          ],
        );
        break;
      case 3:
        return Column(
          children: [
            Container(
              child: Text('Validated'),
            ),
          ],
        );
        break;
      case 4:
        return Column(
          children: [
            Container(
              child: Text('Approved'),
            ),
          ],
        );
        break;
      case 5:
        return Column(
          children: [
            Container(
              child: Text('Rejected'),
            ),
          ],
        );
        break;
      default:
        return Center(
          child: Container(
            child: Text("Something feels fishy! :P"),
          ),
        );
    }
  }
}