After searching a lot, this did the trick for me.
add_action( 'woocommerce_email_after_order_table', 'add_delivery_date_to_admin_new_order', 15, 2 );
function add_delivery_date_to_admin_new_order( $order, $is_admin_email ) {
if ( $is_admin_email ) {
echo '<p>Delivery Date: ' . $order->order_custom_fields['Delivery Date'][0] . '</p>';
echo '<p>Sales Tax: ' . $order->order_tax . '</p>';
echo '<p>Shipping Tax: ' . $order->order_shipping_tax . '</p>';
}
}