TabBarView with variable height inside a ListView

You don’t need to have TabView to show Tabs content.
the minus of this approcach that you are loosing animations and swipes, so you will need to do it by your self if you realy will need it.

class MyHomePage extends StatefulWidget {
  @override
  _MyHomePageState createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> with SingleTickerProviderStateMixin {
  final List<Widget> myTabs = [
    Tab(text: 'one'),
    Tab(text: 'two'),
    Tab(text: 'three'),
  ];

  TabController _tabController;

  @override
  void dispose() {
    _tabController.dispose();
    super.dispose();
  }

  @override
  void initState() {
    _tabController = TabController(length: 3, vsync: this);
    _tabController.addListener(_handleTabSelection);
    super.initState();
  }

  _handleTabSelection() {
    if (_tabController.indexIsChanging) {
      setState(() {});
    }
  }

  _listItem() {
    return Container(
      decoration: BoxDecoration(
        border: Border.all(
          width: 1,
          color: Colors.blueAccent,
        ),
      ),
      height: 120,
      child: Center(
        child: Text('List Item', style: TextStyle(fontSize: 20.0)),
      ),
    );
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: ListView(
        children: <Widget>[
          _listItem(),
          TabBar(
            controller: _tabController,
            labelColor: Colors.redAccent,
            tabs: myTabs,
          ),
          Center(
            child: [
              Text('first tab'),
              Column(
                children: [
                  Text('second tab'),
                  ...List.generate(10, (index) => Text('line: $index'))
                ],
              ),
              Column(
                children: [
                  Text('third tab'),
                  ...List.generate(20, (index) => Text('line: $index'))
                ],
              ),
            ][_tabController.index],
          ),
          _listItem(),
          _listItem(),
        ],
      ),
    );
  }
}