Getting BuildContext in Flutter for localization

No, there is no other way because it is stored using an InheritedWidget, which is a part of the build tree and thus can only be accessed with a reference to it (the BuildContext).
You will need to pass your context to somewhere deep in your model.

Yes there is. You don't need BuildContext to access strings. Here is my solution:

class Strings {
  Strings._(Locale locale) : _localeName = locale.toString() {
    current = this;
  }

  final String _localeName;

  static Strings current;

  static Future<Strings> load(Locale locale) async {
    await initializeMessages(locale.toString());
    final result = Strings._(locale);
    return result;
  }

  static Strings of(BuildContext context) {
    return Localizations.of<Strings>(context, Strings);
  }

  String get title {
    return Intl.message(
      'Hello World',
      name: 'title',
      desc: 'Title for the Demo application',
    );
  }
}

Future<Null> main() async {
  final Locale myLocale = Locale(window.locale);
  await Strings.load(myLocale);
  runApp(MyApplication());
}

Now you can reference a string as follows:

final title = Strings.current.title;