PageView + AnimateToPage

main.dart

import "package:flutter/material.dart";

void main()=> runApp(new MaterialApp(home: MyApp(),),);

class MyApp extends StatefulWidget {
  @override
  _MyAppState createState() => _MyAppState();
}

class _MyAppState extends State<MyApp> with SingleTickerProviderStateMixin {
  PageController _controller;

  static final List<Widget> _widgets = [
    Container(color: Colors.yellowAccent,),
    Container(color: Colors.blueAccent,),
    Container(color: Colors.redAccent,),
    Container(color: Colors.greenAccent,),
  ];

  static const Duration _duration = Duration(milliseconds: 250);
  static const Curve _curve = Curves.easeInOut;

  @override
  void initState() {
    super.initState();
    _controller = PageController();
  }

  @override
  void dispose() {
    _controller.dispose();
    _controller = null;
    super.dispose();
  }

  void _animate2Page() => _controller.animateToPage(
    (_controller.page.toInt()-3).abs() , 
    curve: _curve, 
    duration: _duration,
  );

  @override
  Widget build(BuildContext context) => Scaffold(
    body: PageView(
      controller: _controller,
      children: _widgets,
    ),
    floatingActionButton: FloatingActionButton(
      onPressed: ()=> _animate2Page(),
      child: Icon(Icons.fast_forward),
    ),
  );
}