Add post-formats to post_type 'page'
add_post_type_support( 'page', 'post-formats' );
Next example registers custom post type 'my_custom_post_type', and add Post Formats.
Register custom post type 'my_custom_post_type'
add_action( 'init', 'create_my_post_type' );
function create_my_post_type(...