Adding VAT to WooCommerce

functions.php

/*****************************  FRONTEND  ****************************************/

/**************************
Filter to add a VAT field to:

- My Account - Edit Form -- Billing fields
- Checkout - Edit Form - Billing Fields

This function is also reordering the form fields

Source:  https://docs.woothemes.com/document/tutorial-customising-checkout-fields-using-actions-and-filters
***************************/
function add_woocommerce_billing_fields($billing_fields){

	//reorder woo my billing address form fields
	$billing_fields2['billing_first_name'] = $billing_fields['billing_first_name'];
	$billing_fields2['billing_last_name'] = $billing_fields['billing_last_name'];
 
	$billing_fields2['billing_vat'] = array(
		'type' => 'text',
		'label' =>  __('VAT number',  'keyelp-shop-customization' ),
		'class' => array('form-row-wide'),
		'required' => false,
		'clear' => true
	);
	
	//unimos el resto de campos 
	$merged_billing_fields =  $billing_fields2 + $billing_fields;

	return $merged_billing_fields;
}
add_filter('woocommerce_billing_fields' , 'add_woocommerce_billing_fields');


/*********
Filters to add VAT when printing billing address on:
- (1) My account  
- (2) Checkout - Order Received (after checkout compeltion), 

+++ Additional filters to format the printed output.

********/

// (1) Printing the Billing Address on My Account
add_filter( 'woocommerce_my_account_my_address_formatted_address', 'custom_my_account_my_address_formatted_address', 10, 3 );
function custom_my_account_my_address_formatted_address( $fields, $customer_id, $type ) {

	if ( $type == 'billing' ) {
		$fields['vat'] = get_user_meta( $customer_id, 'billing_vat', true );
	}

	return $fields;
}

// (2) Checkout -- Order Received (printed after having completed checkout)
add_filter( 'woocommerce_order_formatted_billing_address', 'custom_add_vat_formatted_billing_address', 10, 2 );
function custom_add_vat_formatted_billing_address( $fields, $order ) {
	$fields['vat'] = $order->billing_vat;

	return $fields;
}


// Creating merger VAT variables for printing formatting
add_filter( 'woocommerce_formatted_address_replacements', 'custom_formatted_address_replacements', 10, 2 );
function custom_formatted_address_replacements( $address, $args ) {
	$address['{vat}'] = '';
	$address['{vat_upper}']= '';

	if ( ! empty( $args['vat'] ) ) {
		$address['{vat}'] = $args['vat'];
		$address['{vat_upper}'] = strtoupper($args['vat']);
	}
	return $address;
}

//Defining the Spanish formatting to print the address, including VAT.
add_filter( 'woocommerce_localisation_address_formats', 'custom_localisation_address_format' );
function custom_localisation_address_format( $formats ) {
	$formats['ES'] = "{name}\n{company}\n{vat_upper}\n{address_1}\n{address_2}\n{postcode} {city}\n{state}\n{country}";

	return $formats;
}

/*****************************  ADMIN USER PROFILE PAGE  ****************************************/

/*************** 
Filter to add VAT Customer meta fields (user profile field on the billing address grouping)
*****************/
add_filter( 'woocommerce_customer_meta_fields', 'custom_customer_meta_fields' );
function custom_customer_meta_fields( $fields ) {
	$fields['billing']['fields']['billing_vat'] = array(
		'label'       => __( 'VAT number', 'keyelp-shop-customization' )
	);

	return $fields;
}

/***************************  ADMIN ORDER PAGE  ****************************************/

/*********  
Filter to add VAT to the Edit Form on:  Order --  Admin page
*********/
add_filter( 'woocommerce_admin_billing_fields', 'custom_admin_billing_fields' );
function custom_admin_billing_fields( $fields ) {
	$fields['vat'] = array(
		'label' => __( 'VAT number', 'keyelp-shop-customization' ),
		'show'  => true
	);
	
	return $fields;
}


/**************** 
Filter to copy the VAT field from User meta fields to the Order Admin form (after clicking dedicated button on admin page)
******************/

add_filter( 'woocommerce_found_customer_details', 'custom_found_customer_details' );
function custom_found_customer_details( $customer_data ) {
	$customer_data['billing_vat'] = get_user_meta( $_POST['user_id'], 'billing_vat', true );

	return $customer_data;
}

Hello,

I found the solution here about
billing_vat was called incorrectly

add_filter( 'woocommerce_order_formatted_billing_address', 'custom_add_vat_formatted_billing_address', 10, 2 );
function custom_add_vat_formatted_billing_address( $fields, $order ) {
    $fields['vat'] = $order->get_meta('billing_vat');

    return $fields;
}

Hope this will help others :)