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/.gitignore

@@ -0,0 +1,44 @@
+# Miscellaneous
+*.class
+*.log
+*.pyc
+*.swp
+.DS_Store
+.atom/
+.buildlog/
+.history
+.svn/
+migrate_working_dir/
+
+# IntelliJ related
+*.iml
+*.ipr
+*.iws
+.idea/
+
+# The .vscode folder contains launch configuration and tasks you configure in
+# VS Code which you may wish to be included in version control, so this line
+# is commented out by default.
+#.vscode/
+
+# Flutter/Dart/Pub related
+**/doc/api/
+**/ios/Flutter/.last_build_id
+.dart_tool/
+.flutter-plugins
+.flutter-plugins-dependencies
+.packages
+.pub-cache/
+.pub/
+/build/
+
+# Symbolication related
+app.*.symbols
+
+# Obfuscation related
+app.*.map.json
+
+# Android Studio will place build artifacts here
+/android/app/debug
+/android/app/profile
+/android/app/release