Keep VideoPlayerController playing audio when closing the app

Unfortunately Flutter's video_player package doesn't support background video or audio playing. But you can use flutter_playout which wraps ExoPlayer on Android and AVPlayer framework on iOS with the ability to playback video in background or even lock screen. You can find out more about it here. Below is an example code provided by library's GitHub repo which plays a video and it keeps playing in background

import 'dart:io';

import 'package:flutter/material.dart';
import 'package:flutter_playout/multiaudio/HLSManifestLanguage.dart';
import 'package:flutter_playout/multiaudio/MultiAudioSupport.dart';
import 'package:flutter_playout/player_observer.dart';
import 'package:flutter_playout/player_state.dart';
import 'package:flutter_playout/video.dart';
import 'package:flutter_playout_example/hls/getManifestLanguages.dart';

class VideoPlayout extends StatefulWidget {
  final PlayerState desiredState;
  final bool showPlayerControls;

  const VideoPlayout({Key key, this.desiredState, this.showPlayerControls})
      : super(key: key);

  @override
  _VideoPlayoutState createState() => _VideoPlayoutState();
}

class _VideoPlayoutState extends State<VideoPlayout>
    with PlayerObserver, MultiAudioSupport {
  final String _url = null;
  List<HLSManifestLanguage> _hlsLanguages = List<HLSManifestLanguage>();

  @override
  void initState() {
    super.initState();
    Future.delayed(Duration.zero, _getHLSManifestLanguages);
  }

  Future<void> _getHLSManifestLanguages() async {
    if (!Platform.isIOS && _url != null && _url.isNotEmpty) {
      _hlsLanguages = await getManifestLanguages(_url);
      setState(() {});
    }
  }

  @override
  Widget build(BuildContext context) {
    return Container(
      child: Column(
        children: <Widget>[
          /* player */
          AspectRatio(
            aspectRatio: 16 / 9,
            child: Video(
              autoPlay: true,
              showControls: widget.showPlayerControls,
              title: "MTA International",
              subtitle: "Reaching The Corners Of The Earth",
              preferredAudioLanguage: "eng",
              isLiveStream: true,
              position: 0,
              url: _url,
              onViewCreated: _onViewCreated,
              desiredState: widget.desiredState,
            ),
          ),
          /* multi language menu */
          _hlsLanguages.length < 2 && !Platform.isIOS
              ? Container()
              : Container(
                  child: Row(
                    children: _hlsLanguages
                        .map((e) => MaterialButton(
                              child: Text(
                                e.name,
                                style: Theme.of(context)
                                    .textTheme
                                    .button
                                    .copyWith(color: Colors.white),
                              ),
                              onPressed: () {
                                setPreferredAudioLanguage(e.code);
                              },
                            ))
                        .toList(),
                  ),
                ),
        ],
      ),
    );
  }

  void _onViewCreated(int viewId) {
    listenForVideoPlayerEvents(viewId);
    enableMultiAudioSupport(viewId);
  }

  @override
  void onPlay() {
    // TODO: implement onPlay
    super.onPlay();
  }

  @override
  void onPause() {
    // TODO: implement onPause
    super.onPause();
  }

  @override
  void onComplete() {
    // TODO: implement onComplete
    super.onComplete();
  }

  @override
  void onTime(int position) {
    // TODO: implement onTime
    super.onTime(position);
  }

  @override
  void onSeek(int position, double offset) {
    // TODO: implement onSeek
    super.onSeek(position, offset);
  }

  @override
  void onDuration(int duration) {
    // TODO: implement onDuration
    super.onDuration(duration);
  }

  @override
  void onError(String error) {
    // TODO: implement onError
    super.onError(error);
  }
}

I've been using the better_player package. It's quite good uses video_player and chewie and also has support for player notification and PiP.

And don't forget to enable the background audio capability on your xcode. xcode-audio-capability