Flutter Webって書いたけど別にスマホでも動く
こういうやつ

ソース

概要としては
・bottomNavigationBarに普通に３つ並べて真ん中を透明ボタンにする
・floatingActionButtonの領域を広げてFloatingActionButtonを好きな位置に貼る

import 'package:flutter/material.dart';

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

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: MyHomePage(title: 'Flutter Demo Home Page'),
    );
  }
}

class MyHomePage extends StatefulWidget {
  MyHomePage({Key key, this.title}) : super(key: key);

  final String title;

  @override
  _MyHomePageState createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  int _selectedIndex = 0;

  static const TextStyle optionStyle =
      TextStyle(fontSize: 30, fontWeight: FontWeight.bold);

  static const List<Widget> _widgetOptions = <Widget>[
    Text(
      'Index 0: Business',
      style: optionStyle,
    ),
    Text(
      'Index 1: Home',
      style: optionStyle,
    ),
    Text(
      'Index 2: School',
      style: optionStyle,
    ),
  ];

  void _onItemTapped(int index) {
    setState(() {
      _selectedIndex = index;
    });
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text(widget.title),
      ),
      body: SafeArea(
        child: Container(
          color: Colors.white,
          child: Center(
            child: _widgetOptions.elementAt(_selectedIndex),
          ),
        ),
      ),
      bottomNavigationBar: BottomNavigationBar(
        items: [
          BottomNavigationBarItem(
            icon: Icon(Icons.business),
            title: Text('Business'),
          ),
          BottomNavigationBarItem(
            icon: Opacity(
              opacity: 0,
              child: Icon(Icons.home),
            ),
            title: Text(""),
          ),
          BottomNavigationBarItem(
            icon: Icon(Icons.school),
            title: Text('School'),
          ),
        ],
        currentIndex: _selectedIndex,
        selectedItemColor: Colors.amber[800],
        onTap: _onItemTapped,
      ),
      floatingActionButton: Container(
        width: 90,
        height: 100,
        child: FittedBox(
          alignment: Alignment.topCenter,
          child: FloatingActionButton(
            elevation: 0,
            hoverElevation: 0,
            highlightElevation: 0,
            child: Icon(Icons.home),
            backgroundColor: Colors.redAccent,
            onPressed: () {
              _onItemTapped(1);
            },
          ),
        ),
      ),
      floatingActionButtonLocation: FloatingActionButtonLocation.centerDocked,
    );
  }
}