If you are using FBA for your cross-border sales, then you’ll still need to register for VAT where you hold stock. Before selling, you must register in each EU member state where Amazon has warehouses in order to use FBA. Through OSS, you can register in one EU country—typically the one where your inventory is stored—if you sell through your own website as opposed to a marketplace. The VAT owed on items sold within the EU can then be accounted for in this manner.
You still need to register for VAT where you keep stock if you use FBA for international sales. To use FBA, you must first register in each member state of the EU where Amazon operates warehouses.