Add this to your child theme which over-rides what your parent theme supports.
Post Formats for Posts
add_action( 'after_setup_theme', 'wpsites_child_theme_posts_formats', 11 );
function wpsites_child_theme_posts_formats(){
add_theme_support( 'post-formats', array(
'aside',
'audio',
'chat',
'gallery',
'image',
'link',
'quote',
'status',
'video',
) );
}
And here’s the result tested on the Twenty Twelve default theme.
You can also use the above code in your parent themes functions file however the 3rd parameter may not be needed.
To add Post Formats to OTHER Post Types, you’ll also need to add one of the following code snippets on top of the code above.
Post Formats for Custom Post Types
To add Post Formats to Custom Post Types, also add this code to functions and swap cpt-name with the name of your Custom Post Type.
add_post_type_support( 'cpt-name', 'post-formats' );
Post Formats for Pages
To add Post Formats to Pages, also add this code in functions.
add_post_type_support( 'page', 'post-formats' );