Navigating to a new screen when stream value in BLOC changes

You can extend StreamBuilder with custom listener like this:

typedef StreamListener<T> = void Function(T value);

class StreamListenableBuilder<T> extends StreamBuilder<T> {

  final StreamListener<T> listener;

  const StreamListenableBuilder({
    Key key,
    T initialData,
    Stream<T> stream,
    @required this.listener,
    @required AsyncWidgetBuilder<T> builder,
  }) : super(key: key, initialData: initialData, stream: stream, builder: builder);

  @override
  AsyncSnapshot<T> afterData(AsyncSnapshot<T> current, T data) {
    listener(data);
    return super.afterData(current, data);
  }
}

Then connect listener for navigation this way:

StreamListenableBuilder(
    stream: bloc.streamValue,
    listener: (value) {
      if (value==1) {
        Navigator.push(
          context,
          MaterialPageRoute(builder: (context) => SomeNewScreen()),
        );
      }
    },
    builder: (BuildContext context, AsyncSnapshot<int> snapshot) {
      return Container();
    });

You should not use StreamBuilder to handle navigation. StreamBuilder is used to build the content of a screen and nothing else.

Instead, you will have to listen to the stream to trigger side-effects manually. This is done by using a StatefulWidget and overriding initState/dispose as such:

class Example extends StatefulWidget {
  final Stream<int> stream;

  const Example({Key key, this.stream}) : super(key: key);

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

class ExampleState extends State<Example> {
  StreamSubscription _streamSubscription;

  @override
  void initState() {
    super.initState();
    _listen();
  }

  @override
  void didUpdateWidget(Example oldWidget) {
    super.didUpdateWidget(oldWidget);
    if (oldWidget.stream != widget.stream) {
      _streamSubscription.cancel();
      _listen();
    }
  }

  void _listen() {
    _streamSubscription = widget.stream.listen((value) {
      Navigator.pushNamed(context, '/someRoute/$value');
    });
  }

  @override
  void dispose() {
    _streamSubscription.cancel();
    super.dispose();
  }

  @override
  Widget build(BuildContext context) {
    return Container();
  }
}

---

Note that if you're using an InheritedWidget to obtain your stream (typically BLoC), you will want to use didChangeDependencies instead of initState/didUpdateWidget.

This leads to:

class Example extends StatefulWidget {
  @override
  ExampleState createState() => ExampleState();
}

class ExampleState extends State<Example> {
  StreamSubscription _streamSubscription;
  Stream _previousStream;

  void _listen(Stream<int> stream) {
    _streamSubscription = stream.listen((value) {
      Navigator.pushNamed(context, '/someRoute/$value');
    });
  }

  @override
  void didChangeDependencies() {
    super.didChangeDependencies();
    final bloc = MyBloc.of(context);
    if (bloc.stream != _previousStream) {
      _streamSubscription?.cancel();
      _previousStream = bloc.stream;
      _listen(bloc.stream);
    }
  }

  @override
  void dispose() {
    _streamSubscription.cancel();
    super.dispose();
  }

  @override
  Widget build(BuildContext context) {
    return Container();
  }
}