MaterialAppのnavigatorKeyのサンプル https://docs.flutter.io/flutter/material/MaterialApp/navigatorKey.html

navigatorKey_main.dart

import 'package:flutter/material.dart';

void main() {
  final navigatorKey = GlobalKey<NavigatorState>();
  runApp(
    MyApp(
      navigatorKey: navigatorKey,
    ),
  );
}

class MyApp extends StatelessWidget {
  final GlobalKey<NavigatorState> navigatorKey;

  const MyApp({
    Key key,
    @required this.navigatorKey,
  }) : super(key: key);

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
        floatingActionButton: FloatingActionButton(
          child: Icon(Icons.navigate_next),
          onPressed: () {
            // ここだと `Navigator.of(context)` 使えるので意味が無いが
            // 実際にはnavigatorKeyを取り回すことでどこでも呼べる
            navigatorKey.currentState.pushNamed("foo");
          },
        ),
      ),
      navigatorKey: navigatorKey,
      onGenerateRoute: _handleRoutes,
    );
  }

  Route _handleRoutes(RouteSettings settings) {
    final name = settings.name;
    return MaterialPageRoute(
      builder: (context) => Scaffold(
            appBar: AppBar(
              title: Text(name),
            ),
          ),
    );
  }
}

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