Custom WooCommerce shipping Method and distance rate value issue

You need to set the cost to a WC_Session variable to avoid loosing the distance calculated cost value, so your function code should be:

            public function calculate_shipping( $packages = array() ) {                wp_parse_str( $_POST['post_data'], $post_data );                $cURLConnection = curl_init();                curl_setopt($cURLConnection, CURLOPT_URL, $this->url_api.$post_data["distancia_billing"]);                curl_setopt($cURLConnection, CURLOPT_RETURNTRANSFER, true);                $datos = curl_exec($cURLConnection);                curl_close($cURLConnection);                $jsonArrayResponse = json_decode($datos, true);                                if( isset($jsonArrayResponse["precio"]) && ! empty($jsonArrayResponse["precio"]) && isset(WC()->session) ) {                    WC()->session->set('shipping_distance_cost', floatval($jsonArrayResponse["precio"]) );                }                $this->add_rate( array(                    'id'       => $this->id,                    'label'    => $this->title,                    'cost'     => WC()->session->__isset('shipping_distance_cost') ? WC()->session->get('shipping_distance_cost') : '10.00',                    'calc_tax' => 'per_order'                ) );            }

But you should need to remove that session variable when order has been created, so outside your shipping class code, add the following:

add_action( 'woocommerce_checkout_order_created', 'remove_wc_session_shipping_distance_cost' );function remove_wc_session_shipping_distance_cost( $order ) {    if ( WC()->session->__isset('shipping_distance_cost') ) {        WC()->session->__unset('shipping_distance_cost')    }}

It should work.