It is indeed possible to use custom URL schemes for authentication in an iOS app. Here are the steps I took:
Choose an arbitrary domain, like stackexchange.com, for the OAuth domain in your Stack Apps
(Optional) Make sure it has a Stack Apps Post if you want tokens with write access.
Check the checkboxes for these options:
Enable Client Side OAuth Flow
When using the API to add/edit posts or comments, you need to ensure the preview parameter is set to false, otherwise it's just a 'test' request which does nothing (but allows you to test if the response parsing on your side works correctly). Just like writing content on the site itself, the body needs to be in Markdown.
If you set preview to false, you'll ...