Use different color of the status bar and color of the app bar.

main.dart

import 'dart:io';

import 'package:flutter/material.dart';
import 'package:flutter/services.dart';

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

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      routes: <String, WidgetBuilder>{
        'Page 1': (BuildContext context) => MyHomePage(),
        'Page 2': (BuildContext context) => MyHomePage2(),
      },
      theme: ThemeData(
        visualDensity: VisualDensity.adaptivePlatformDensity,
      ),
      home: MyHomePage(),
    );
  }
}

class MyHomePage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return AnnotatedRegion<SystemUiOverlayStyle>(
      value: SystemUiOverlayStyle(
        statusBarColor: Colors.black,
        statusBarBrightness: Brightness.dark,
        statusBarIconBrightness: Brightness.light,
      ),
      child: Scaffold(
        appBar: Platform.isIOS
            ? AppBar(
                brightness: Brightness.dark,
                elevation: 0.0,
                backgroundColor: Colors.black,
                toolbarHeight: 0.0,
              )
            : null,
        body: SafeArea(
          child: Column(
            children: [
              AppBar(
                title: Text('Page 1'),
                backgroundColor: Colors.green,
              ),
              Center(
                child: MaterialButton(
                  onPressed: () {
                    Navigator.pushNamed(context, 'Page 2');
                  },
                  child: Text('Next Page'),
                ),
              ),
            ],
          ),
        ),
      ),
    );
  }
}

class MyHomePage2 extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return AnnotatedRegion<SystemUiOverlayStyle>(
      value: SystemUiOverlayStyle(
        statusBarColor: Colors.white,
        statusBarBrightness: Brightness.light,
        statusBarIconBrightness: Brightness.dark,
      ),
      child: Scaffold(
        appBar: Platform.isIOS
            ? AppBar(
                brightness: Brightness.light,
                elevation: 0.0,
                backgroundColor: Colors.white,
                toolbarHeight: 0.0,
              )
            : null,
        body: SafeArea(
          child: Column(
            children: [
              AppBar(
                title: Text('Page 2'),
                backgroundColor: Colors.red,
              ),
              Center(
                child: Text('Page 2'),
              ),
            ],
          ),
        ),
      ),
    );
  }
}