Как сделать Tabs внутри AppBar как у ВКонтакте?

Вот так можно (в Dartpad'е можно попробовать):

import 'package:flutter/material.dart';

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

class TabbedAppBarSample extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: DefaultTabController(
        length: choices.length,
        child: Scaffold(
          appBar: AppBar(
            title: Row(
              mainAxisAlignment: MainAxisAlignment.spaceBetween,
              children: [
                IconButton(
                  icon: Icon(Icons.camera_alt),
                  onPressed: () {},
                ),
                TabBar(
                  isScrollable: true,
                  tabs: choices.map((Choice choice) {
                    return Tab(
                      text: choice.title,
                    );
                  }).toList(),
                ),
                IconButton(
                  icon: Icon(Icons.add_alert),
                  onPressed: () {},
                ),
              ],
            ),
          ),
          body: TabBarView(
            children: choices.map((Choice choice) {
              return Padding(
                padding: const EdgeInsets.all(16.0),
                child: ChoiceCard(choice: choice),
              );
            }).toList(),
          ),
        ),
      ),
    );
  }
}

class Choice {
  const Choice({this.title, this.icon});

  final String title;
  final IconData icon;
}

const List<Choice> choices = const <Choice>[
  const Choice(title: 'CAR', icon: Icons.directions_car),
  const Choice(title: 'BICYCLE', icon: Icons.directions_bike),
  const Choice(title: 'BOAT', icon: Icons.directions_boat),
  const Choice(title: 'BUS', icon: Icons.directions_bus),
  const Choice(title: 'TRAIN', icon: Icons.directions_railway),
  const Choice(title: 'WALK', icon: Icons.directions_walk),
];

class ChoiceCard extends StatelessWidget {
  const ChoiceCard({Key key, this.choice}) : super(key: key);

  final Choice choice;

  @override
  Widget build(BuildContext context) {
    return Card(
      color: Colors.white,
      child: Center(
        child: Column(
          mainAxisSize: MainAxisSize.min,
          crossAxisAlignment: CrossAxisAlignment.center,
          children: <Widget>[
            Icon(choice.icon, size: 128.0),
            Text(choice.title),
          ],
        ),
      ),
    );
  }
}