$post_ids = get_user_meta( 123, 'mbfp_posts', true ); //123 is the user ID
You can contact Bricks support and ask them how to get the user ID in the loop.
If you are not able to complete the task, we offer a customization service with an extra fee. Please contact us here for more details https://metabox.io/contact/
I just understand the user ID is the author of the post in the loop. For non-logged-in users, you can get the posts from the cookie. Please take a look at the file /wp-content/plugins/mb-favorite-posts/src/Helper.php