Calculate shipping methods/rates within an existing order in WooCommerce

Ok so thanks to @mujuonly, I was able to figure it out.

Here's how to get all calculated shipping rates, the same way it's shown on the cart page.

// Post variables
$order_id   = isset($_POST['order_id'])?$_POST['order_id']:0;
$country    = isset($_POST['country'])?$_POST['country']:0;
$state      = isset($_POST['state'])?$_POST['state']:0;
$postcode   = isset($_POST['postcode'])?$_POST['postcode']:0;
$city       = isset($_POST['city'])?$_POST['city']:0;

// Order and order items
$order          = wc_get_order( $order_id );
$order_items    = $order->get_items();

// Reset shipping first
WC()->shipping()->reset_shipping();

// Set correct temporary location
if ( $country != '' ) {
    WC()->customer->set_billing_location( $country, $state, $postcode, $city );
    WC()->customer->set_shipping_location( $country, $state, $postcode, $city );
} else {
    WC()->customer->set_billing_address_to_base();
    WC()->customer->set_shipping_address_to_base();
}

// Remove all current items from cart
if ( sizeof( WC()->cart->get_cart() ) > 0 ) {
    WC()->cart->empty_cart();
}

// Add all items to cart
foreach ($order_items as $order_item) {
    WC()->cart->add_to_cart($order_item['product_id'], $order_item['qty']);
}

// Calculate shipping
$packages = WC()->cart->get_shipping_packages();
$shipping = WC()->shipping->calculate_shipping($packages);
$available_methods = WC()->shipping->get_packages();

$available_methods[0]['rates'] will have all the shipping rates that are available to that location for products inside the order.

Try using:

// Calculate totals
WC()->cart->calculate_totals();
WC()->cart->calculate_shipping();

// Retrieve the shipping total
$shipping_total = WC()->cart->get_shipping_total();

The WC_Cart class should have all of the methods you would need to recreate any cart functionality you might need. I suggest that you should read through and familiarize yourself with the class definition here...

https://docs.woocommerce.com/wc-apidocs/class-WC_Cart.html