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/ios/.gitignore

@@ -0,0 +1,34 @@
+**/dgph
+*.mode1v3
+*.mode2v3
+*.moved-aside
+*.pbxuser
+*.perspectivev3
+**/*sync/
+.sconsign.dblite
+.tags*
+**/.vagrant/
+**/DerivedData/
+Icon?
+**/Pods/
+**/.symlinks/
+profile
+xcuserdata
+**/.generated/
+Flutter/App.framework
+Flutter/Flutter.framework
+Flutter/Flutter.podspec
+Flutter/Generated.xcconfig
+Flutter/ephemeral/
+Flutter/app.flx
+Flutter/app.zip
+Flutter/flutter_assets/
+Flutter/flutter_export_environment.sh
+ServiceDefinitions.json
+Runner/GeneratedPluginRegistrant.*
+
+# Exceptions to above rules.
+!default.mode1v3
+!default.mode2v3
+!default.pbxuser
+!default.perspectivev3