画面遷移後の処理例

main.dart

import 'package:flutter/material.dart';

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

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      home: HomePage(),
    );
  }
}

class HomePage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(title: const Text('TEST')),
      body: Center(
          child: FlatButton(
        child: Text("to B"),
        onPressed: () => Navigator.of(context).push(
            MaterialPageRoute(builder: (BuildContext context) => ScreenB())),
      )),
    );
  }
}

class ScreenB extends StatefulWidget {
  @override
  _ScreenBState createState() => _ScreenBState();
}

class _ScreenBState extends State<ScreenB> {
  @override
  void initState() {
    super.initState();
    Future.delayed(Duration(seconds: 3)).then(
      ((_) => showDialog(
          context: context,
          builder: (context) {
            return AlertDialog(
              content: Container(
                child: Text("dialog"),
              ),
            );
          })),
    );
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text("Screen B"),
      ),
      body: Center(
        child: Text("HI."),
      ),
    );
  }
}