From function Widget to StatelessWidget in Flutter

It's simple. Take a look at the source code and read the comments. The source is auto explained by itself. I have used your methods names as class names.

// the method buildList into a stateless widgetclass BuildListWidget extends StatelessWidget{  final List<DocumentSnapshot> snapshotList;  BuildListWidget({this.snapshotList}){} // you can use this approach to initialize your snapshotList.   // Here there parameter is already the member of class snapshotList  @override  Widget build(BuildContext context) {    //building a listView in this way allows you build items on demand.    return ListView.builder(        itemCount: snapshotList.length, // number of items in list        itemBuilder: (BuildContext context, int index){          //creating list members. Each one with your DocumentSnapshot from list          return BuildListItemWidget(            dataSnapshot: snapshotList[index], // getting DocumentSnapshot from list          );        }    );  }}// the mehtod _buildListItem into a stateless widgetclass BuildListItemWidget extends StatelessWidget {  final DocumentSnapshot _data; // just if you want to hold a snapshot...  final Record _record; // your record reference//here another approach to inicialize class data using named parameters and// initialization list in class contructor  BuildListItemWidget({@required DocumentSnapshot dataSnapshot}) :      _record = Record.fromSnapshot(dataSnapshot),      _data = dataSnapshot;  @override  Widget build(BuildContext context) {    return Column(        children: <Widget>[          Text(record.title),          YoutubePlayer(source: _record.videoId.toString(),            quality: YoutubeQuality.LOW,            autoPlay: false,            context: context          );    }}// usage...class _VideoListState extends State<VideoList> {  @override  Widget build(BuildContext context) {    ...    body: StreamBuilder<QuerySnapshot>(    stream: Firestore.instance.collection(widget.category).snapshots(),    builder: (context, snapshot) {    if (!snapshot.hasData) return LinearProgressIndicator();    // so here you have a statelessWidget    return  BuildListWidget( snapshotList: snapshot.data.documents );    },    ),  }}