This code generates a screen with a custom bidirectional and infinite scrollable PageView in Flutter. Replace your own assets names. More details can be found on Medium. https://medium.com/p/dfff43649c23/edit

main.dart

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

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

class CustomPageViewApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    SystemChrome.setPreferredOrientations([
      DeviceOrientation.portraitUp,
      DeviceOrientation.portraitDown,
    ]);
    return MaterialApp(
      title: 'Custom PageView',
      home: CustomPageViewScreen(),
    );
  }
}

class CustomPageViewScreen extends StatefulWidget {
  @override
  _CustomPageViewScreenState createState() => new _CustomPageViewScreenState();
}

class _CustomPageViewScreenState extends State<CustomPageViewScreen> {
  List interests = [
    InterestsModel('Snowboarding', 'assets/ic_snowboarding_gray.png'),
    InterestsModel('BMX', 'assets/ic_bike_gray.png'),
    InterestsModel('Skateboarding', 'assets/ic_skateboarding_gray.png')
  ];

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Container(
          color: Color.fromRGBO(36, 43, 47, 1),
          child: Column(
            mainAxisAlignment: MainAxisAlignment.center,
            children: <Widget>[
              _buildTitle(),
              _buildInterestsContent(),
              _buildCheckIcon(),
              _buildNextButton()
            ],
          )),
    );
  }

  Text _buildTitle() {
    return Text(
      "Choose your interests".toUpperCase(),
      textAlign: TextAlign.center,
      style: TextStyle(
          color: Color.fromRGBO(243, 243, 243, 1),
          fontSize: 19,
          fontFamily: 'RadikalMedium'),
    );
  }

  Stack _buildInterestsContent() {
    return Stack(
      children: <Widget>[
        _buildInterestsPageView(),
        Row(
          mainAxisAlignment: MainAxisAlignment.spaceBetween,
          children: <Widget>[
            Image.asset('assets/bg_gradient_left.png'),
            Image.asset('assets/bg_gradient_right.png'),
          ],
        ),
      ],
    );
  }

  List selectedInterests = [];
  PageController pageController =
      PageController(viewportFraction: 0.45, initialPage: 4240);

  Container _buildInterestsPageView() {
    return Container(
      height: 210,
      child: PageView.builder(
        itemBuilder: (context, int currentIdx) {
          int crt = currentIdx;
          if (crt > 2) {
            if (crt % 3 == 0) {
              crt = 0;
            } else if ((crt + 1) % 3 == 0) {
              crt = 2;
            } else if ((crt - 1) % 3 == 0) {
              crt = 1;
            }
          }
          return Container(
            margin: const EdgeInsets.only(top: 31.0),
            child: _buildPageViewItem(interests[crt], crt),
          );
        },
        controller: pageController,
      ),
    );
  }

  GestureDetector _buildPageViewItem(InterestsModel data, int crt) {
    bool active = selectedInterests.contains(crt);
    final String backgroundAsset = active
        ? 'assets/bg_yellow_bordered.png'
        : 'assets/bg_gray_bordered.png';
    return GestureDetector(
      onTap: () {
        setState(() {
          if (selectedInterests.contains(crt))
            selectedInterests.remove(crt);
          else {
            selectedInterests.add(crt);
          }
        });
      },
      child: Column(
        children: <Widget>[
          Text(data.title.toUpperCase(),
              style: TextStyle(
                color: Color.fromRGBO(243, 243, 243, 1),
                fontFamily: 'RadikalThin',
                fontSize: 11.0,
              )),
          SizedBox(
              height: 129,
              width: 129,
              child: Container(
                margin: const EdgeInsets.only(top: 5),
                decoration: BoxDecoration(
                    image: DecorationImage(image: AssetImage(backgroundAsset))),
                child: Image.asset(data.imageAsset),
              )),
        ],
      ),
    );
  }

  Container _buildCheckIcon() {
    String buttonAsset = selectedInterests.isEmpty
        ? 'assets/ic_check_gray.png'
        : 'assets/ic_check_yellow_rounded.png';
    return Container(
      child: Image.asset(buttonAsset),
    );
  }

  Container _buildNextButton() {
    return Container(
      alignment: Alignment.center,
      margin: const EdgeInsets.only(left: 71, right: 71, top: 21),
      child: SizedBox(
        width: double.infinity,
        height: 45,
        child: RaisedButton(
          child: Text(
            "Next".toUpperCase(),
            style: TextStyle(
                color: Color.fromRGBO(40, 48, 52, 1),
                fontFamily: 'RadikalMedium',
                fontSize: 19),
          ),
          color: Colors.white,
          elevation: 4.0,
          onPressed: () {},
        ),
      ),
    );
  }
}

class InterestsModel {
  String imageAsset;
  String title;

  InterestsModel(this.title, this.imageAsset);
}