We can only export the 10 most recently updated addresses per customer record in Shopify (this is all the API allows).

To export these addresses, simply select the field addresses when creating a Data Settings for Customer data.  This will export a list of addresses in JSON format in one column.

If you'd like to export the data in a more readable format, you can use this formula in the Calculated Fields section:

"\n\n".join([((i.first_name) + " " + (i.last_name) + "\n" + (i.address1 or "") + "\n" + ((i.address2 + "\n") if i.address2 else "") + (i.city or "") + ", " + (i.province or "") + " " + (i.zip or "") + "\n" + i.country) for i in load_json_data({{ addresses }}) if i.country])

This will export each address in this format separated by 2 line breaks:

Full Name
Address1
Address2
City, State/Province Zip
Country