Edit php files in subdirs in a child theme

Any suggestions?

For one, read and interpret the error message.
“Cannot redeclare require_once_child()” is pretty straightforward: Don’t give two functions the same name.

I am uncertain whether your general idea is sensible in the first place, but should it be, this

function require_once_child() {
    require_once('includes/sf-content-display/sf-post-formats.php');    
}
add_action( 'init', 'require_once_child' );

is all you need.