It's a bit hard to use a regular Scaffold Drawer without the regular scaffold controls, as far as I can tell.
I came up with a solution for your problem, if I understood it correctly. Looks a lot like the spec site, needs a bit of styling.
Took the example from the NavigationRail documentation and added a Visibility widget. Now clicking on the destinations, you can show and hide their child widgets(drawer). No drawer animation though.

import 'package:flutter/material.dart';
void main() => runApp(const MyApp());
class MyApp extends StatelessWidget {
const MyApp({super.key});
@override
Widget build(BuildContext context) {
return MaterialApp(
theme: ThemeData(
colorSchemeSeed: const Color(0xff6750a4), useMaterial3: true),
home: const NavRailExample(),
);
}
}
class NavRailExample extends StatefulWidget {
const NavRailExample({super.key});
@override
State<NavRailExample> createState() => _NavRailExampleState();
}
class _NavRailExampleState extends State<NavRailExample> {
int _selectedIndex = 0;
NavigationRailLabelType labelType = NavigationRailLabelType.all;
bool showLeading = false;
bool showTrailing = false;
double groupAligment = -1.0;
bool _isClosed = false;
Widget _getWidget(int index) {
switch (index) {
case 1:
return GestureDetector(
child: const Text('Tap!'),
onTap: () => setState(() {
_isClosed = true;
}),
);
case 2:
return const Text('empty');
default:
return ListView(
children: const [
ExpansionTile(
title: Text('whatev'),
children: [Text('1'), Text('2')],
),
ListTile(
title: Text('adfafdafaf'),
)
],
);
}
}
Widget _getPage(int index) {
switch (index) {
case 1:
return const Center(child: Text('sheeesh'));
case 2:
return const Center(child: Text('empty'));
default:
return const Center(child: Text('yolo'),);
}
}
@override
Widget build(BuildContext context) {
return Scaffold(
body: SafeArea(
child: Row(
children: <Widget>[
NavigationRail(
selectedIndex: _selectedIndex,
groupAlignment: groupAligment,
onDestinationSelected: (int index) {
setState(() {
_isClosed = (_selectedIndex == index || _isClosed)
? !_isClosed
: _isClosed;
_selectedIndex = index;
});
},
labelType: labelType,
leading: showLeading
? FloatingActionButton(
elevation: 0,
onPressed: () {
// Add your onPressed code here!
},
child: const Icon(Icons.add),
)
: const SizedBox(),
trailing: showTrailing
? IconButton(
onPressed: () {
// Add your onPressed code here!
},
icon: const Icon(Icons.more_horiz_rounded),
)
: const SizedBox(),
destinations: const <NavigationRailDestination>[
NavigationRailDestination(
icon: Icon(Icons.favorite_border),
selectedIcon: Icon(Icons.favorite),
label: Text('First'),
),
NavigationRailDestination(
icon: Icon(Icons.bookmark_border),
selectedIcon: Icon(Icons.book),
label: Text('Second'),
),
NavigationRailDestination(
icon: Icon(Icons.star_border),
selectedIcon: Icon(Icons.star),
label: Text('Third'),
),
],
),
Visibility(
maintainState: false,
visible: !_isClosed,
child: Row(
children: [
const VerticalDivider(thickness: 1, width: 1),
SizedBox(
height: double.infinity,
width: 200,
child: _getWidget(_selectedIndex),
)
],
),
),
const VerticalDivider(thickness: 1, width: 1),
// This is the main content.
Expanded(
child: _getPage(_selectedIndex),
),
],
),
),
);
}
}