When I set a slug and update the post, the slug gets uploaded and saved.
When I set a slug and update the post, the slugs gets cleared as soon as I leave the editor.
Emulator, Android 9
We've investigated this issue with @ashiagr. We don't send the slug to the API (wp.editPost action -> it gets lost during the transformation from PostModel to the request here). We've also checked the documentation and it seems slug parameter isn't even supported. However, the documentation mentions string post_name: Encoded URL (slug) so we are wondering if we could use it or if it serves a different purpose.
As a next step I'd suggest checking how iOS handles slugs on self-hosted sites and we'll see where it leads us.
Tested on iOS app. Slug was properly saved on a self-hosted site. iOS app is using post_name parameter for the slug.

As discussed, we'll have to support this parameter in the requests for Android app and make changes to the wordpress-mobile/WordPress-FluxC-Android/