My site's theme has a featured post slider feature that displays a sliding carousel of posts that are flagged as "featured." There is a checkbox on the WordPress editor page for this purpose (see attachment).
The thing is, it only works for posts. I want to be able to feature posts from the custom post types I created with Types to show up in this carousel.
I have already approached the theme author about it, and they are unwilling to help, saying that they don't do customizations.
I was wondering if you'd be able to help me surmount this?
Well, the best people to solve it would certainly be the theme authors, as it is a theme feature, and all you are asking is that it work with custom post types (which are a WordPress feature, not a proprietary Toolset feature).
There are two parts to the problem.
The first would be modifying the post types for which the post option with the featured checkbox UI is displayed. The option itself is probably just saved in wp_postmeta for each post.
The second would be modifying the query which retrieves the featured posts to show in the slider, which would likely be a simple question of updating the query argument for post_type to include the slug of your custom post type(s).
It shouldn't be too difficult using either filters (if they provide them) or modifying their code in a child theme, but I can't help you with it, I'm afraid, because it isn't really a Toolset issue.