Wordpress - Get featured image on Blog Index

if you are referring to the 'page for posts', then try (only relevant section of your code shown):

if (is_home() && get_option('page_for_posts') ) {
    $img = wp_get_attachment_image_src(get_post_thumbnail_id(get_option('page_for_posts')),'full'); 
    $featured_image = $img[0];
} else { 

I'd suggest anyone doing this consider the following adjustments:

1. Get the ID of the current page/post/index using get_queried_object(). For a blog index that's set to a page this will return the correct page ID.
2. If all you want is the full-sized image use wp_get_attachment_url() instead of wp_get_attachment_image_src()

Here's a quick function I'd use to achieve this in a simpler way:

/**
 * Custom Featured Image
 */
function custom_featured_image() {
    $queried_obj = get_queried_object();

    // Don't use on single posts (JUST FOR THIS DEMO)
    if ( is_single() ) return;

    // Get the featured image ID
    $image_id = get_post_thumbnail_id( $queried_obj->ID );

    // Get the URL for the full sized image
    $image_src = wp_get_attachment_url( $image_id );

    return $image_src;
}

I personally like to avoid excessive nested conditional logic, using a function can help with this.