Next Gen UI demo (#1778)

First pass at a Next Generation UI demo app. The UI needs work, feedback
gratefully accepted.

## Pre-launch Checklist

- [x] I read the [Flutter Style Guide] _recently_, and have followed its
advice.
- [x] I signed the [CLA].
- [x] I read the [Contributors Guide].
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-devrel
channel on [Discord].

<!-- Links -->
[Flutter Style Guide]:
https://github.com/flutter/flutter/wiki/Style-guide-for-Flutter-repo
[CLA]: https://cla.developers.google.com/
[Discord]: https://github.com/flutter/flutter/wiki/Chat
[Contributors Guide]:
https://github.com/flutter/samples/blob/main/CONTRIBUTING.md

next_gen_ui_demo/linux/my_application.h

@@ -0,0 +1,18 @@
+#ifndef FLUTTER_MY_APPLICATION_H_
+#define FLUTTER_MY_APPLICATION_H_
+
+#include <gtk/gtk.h>
+
+G_DECLARE_FINAL_TYPE(MyApplication, my_application, MY, APPLICATION,
+                     GtkApplication)
+
+/**
+ * my_application_new:
+ *
+ * Creates a new Flutter-based application.
+ *
+ * Returns: a new #MyApplication.
+ */
+MyApplication* my_application_new();
+
+#endif  // FLUTTER_MY_APPLICATION_H_