When creating/editing a Data Settings for Order data, simply select the field below to export the tax ID associated with the customer record:

• customer.tax_settings.tax_id

This tax ID field is the "VAT number" shown under "Tax details" in the Shopify Admin when viewing a customer from the UK/EU:

Note that this will export the customer's current tax ID (at the time export).  There's no historical tax ID field at the order level.