how to get selected index of dropdownbutton in flutter

You should probably use a custom model object (e.g. User) as the type for DropdownButton.

import 'package:flutter/material.dart';

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

class User {
  const User(this.name);    
  final String name;
}

class MyApp extends StatefulWidget {
  State createState() => new MyAppState();
}

class MyAppState extends State<MyApp> {
  User selectedUser;
  List<User> users = <User>[User('Foo'), User('Bar')];    
  @override
  Widget build(BuildContext context) {
    return new MaterialApp(
      home: new Scaffold(
        body: new Center(
          child: new DropdownButton<User>(
            hint: new Text("Select a user"),
            value: selectedUser,
            onChanged: (User newValue) {
              setState(() {
                selectedUser = newValue;
              });
            },
            items: users.map((User user) {
              return new DropdownMenuItem<User>(
                value: user,
                child: new Text(
                  user.name,
                  style: new TextStyle(color: Colors.black),
                ),
              );
            }).toList(),
          ),
        ),
      ),
    );
  }
}

Similar to Collin Jackson's answer, you can simply use a List of Strings and check the indexOf to set the value, which might be preferable in some situations rather than making a User class. If you want to set an initial value set _user to an integer value when defined.

int _user;
...

var users = <String>[
  'Bob',
  'Allie',
  'Jason',
];

return new DropdownButton<String>(
  hint: new Text('Pickup on every'),
  value: _user == null ? null : users[_user],
  items: users.map((String value) {
    return new DropdownMenuItem<String>(
      value: value,
      child: new Text(value),
    );
  }).toList(),
  onChanged: (value) {
    setState(() {
      _user = users.indexOf(value);
    });
  },
);