The response you're getting from facebook itself says that the user with the access to the page you're trying to DELETE
the post of, doesn't have the right permissions to do so.
This is because your account/user doesn't hold a role which gives rights to delete the posts from the page. The account must be holding one of these roles - Moderator
, Advertiser
, Insights Analyst
. Only the Manager
and the Content Creator
has rights to delete posts from the pages.
Hence, you should either get one of those roles (The admin can change the role for you) or authenticate the app from a Manager/Content Creator's account.
For more details, you can check out their official help section - What are the different kinds of Page admins and what can they do?
Hope that helps!