Example Stack AppBar

main.dart

import 'package:flutter/material.dart';

const Color darkBlue = Color.fromARGB(255, 18, 32, 47);

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

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      theme: ThemeData.dark().copyWith(
        scaffoldBackgroundColor: darkBlue,
      ),
      debugShowCheckedModeBanner: false,
      home: Scaffold(
        appBar: PreferredSize(
          preferredSize: Size.fromHeight(100),
          child: Stack(
            fit: StackFit.expand,
            children: <Widget>[
              Container(
                color: Colors.blue,
              ),
              Positioned(
                top: 16,
                left: 16,
                child: Text("Verdansk"),
              ),
              Positioned(
                top: 36,
                left: 16,
                child: Text("BR Quads"),
              ),
            ],
          ),
        ),
        body: Center(
          child: MyWidget(),
        ),
      ),
    );
  }
}

class MyWidget extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Text(
      'Hello, World!',
      style: Theme.of(context).textTheme.headline4,
    );
  }
}