ProgressDialogNavDiffScreens.dart

import 'package:flutter/material.dart';
import 'package:progress_dialog/progress_dialog.dart';

ProgressDialog pr;

void main() {
  runApp(MaterialApp(
    home: FirstScreen(),
  ));
}

class FirstScreen extends StatefulWidget {
  @override
  _FirstScreenState createState() => _FirstScreenState();
}

class _FirstScreenState extends State<FirstScreen> {
  ProgressDialog pr;

  @override
  Widget build(BuildContext context) {
    pr = new ProgressDialog(context);
    pr.style(message: 'Please wait...');

    return Scaffold(
      body: Center(
        child: RaisedButton(
          child: Text('Show dialog and go to next screen',
              style: TextStyle(color: Colors.white)),
          color: Colors.blueAccent,
          onPressed: () {
            pr.show();
            Future.delayed(Duration(seconds: 3)).then((value) {
              pr.hide().whenComplete(() {
                Navigator.of(context).push(CupertinoPageRoute(
                    builder: (BuildContext context) => SecondScreen()));
              });
            });
          },
        ),
      ),
    );
  }
}

class SecondScreen extends StatefulWidget {
  @override
  _SecondScreenState createState() => _SecondScreenState();
}

class _SecondScreenState extends State<SecondScreen> {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Center(child: Text('I am second screen')),
    );
  }
}