Look Through Family Tree and Find Featured Image

I don’t see anything particularly wrong with it, although I’d probably write the loop like this:

$featuredImage="";
foreach ( $familyTree as $family_postid ) {
    if ( has_post_thumbnail( $family_postid ) ) {
        $featuredImage = get_the_post_thumbnail( $family_postid, 'full' );
        break;
    }
}

A bit simpler to understand and eliminates the use of the counter and boolean found variables.