reproNestedTabsSample.dart

import 'package:flutter/material.dart';

void main() => runApp(new MyApp());

class MyApp extends StatefulWidget {
  @override
  _MyAppState createState() => new _MyAppState();
}

class _TabBarContainer extends StatelessWidget {
  final TabController tabController;

  _TabBarContainer({
    this.tabController,
  });

  @override
  Widget build(BuildContext context) {
    return Container(
      color: Colors.blue,
      child: Column(
        children: <Widget>[
          TabBar(
            controller: tabController,
            tabs: [
              Tab(text: "Yellow"),
              Tab(text: "Grey"),
            ],
          ),
          Expanded(
            flex: 1,
            child: TabBarView(
              controller: tabController,
              children: <Widget>[
                Container(color: Colors.yellow),
                Container(color: Colors.grey),
              ],
            ),
          )
        ],
      ),
    );
  }
}

class _MyAppState extends State<MyApp> with TickerProviderStateMixin {
  TabController _mainTabController;
  TabController _nestedTabController;

  @override
  void initState() {
    super.initState();
    _mainTabController = TabController(length: 4, vsync: this);
    _nestedTabController = TabController(length: 2, vsync: this);
  }

  @override
  dispose() {
    _mainTabController.dispose();
    _nestedTabController.dispose();
    super.dispose();
  }

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: new Scaffold(
        appBar: AppBar(
          title: Text('Exception for Nested Tabs'),
          bottom: TabBar(
            controller: _mainTabController,
            tabs: <Widget>[
              Tab(icon: Icon(Icons.add), text: "Tab"),
              Tab(icon: Icon(Icons.add), text: "Tab"),
              Tab(icon: Icon(Icons.add), text: "Tab"),
              Tab(icon: Icon(Icons.add), text: "Tab"),
            ],
          ),
        ),
        body: TabBarView(
          controller: _mainTabController,
          children: <Widget>[
            Container(color: Colors.red),
            _TabBarContainer(tabController: _nestedTabController),
            Container(color: Colors.green),
            Container(color: Colors.indigo),
          ],
        ),
      ),
    );
  }
}