SystemChrome.setEnabledSystemUIOverlays([]) should do what you want.
You can bring it back with SystemChrome.setEnabledSystemUIOverlays(SystemUiOverlay.values).
Import it using
import 'package:flutter/services.dart';
Update answer (from Flutter 2.5 or latest):
SystemChrome.setEnabledSystemUIMode(SystemUiMode.leanBack);
Or you can use another options like:
SystemChrome.setEnabledSystemUIMode(SystemUiMode.manual, overlays: [
  SystemUiOverlay.bottom
]);  // to hide only bottom bar
Then when you need to re-show it (like when dispose) use this:
  @override
  void dispose() {
    super.dispose();
    SystemChrome.setEnabledSystemUIMode(SystemUiMode.manual, overlays: SystemUiOverlay.values);  // to re-show bars
  }
