To dropship via Amazon, you need to follow Amazon's terms and policies.
Please check the links below:
Amazon Prime isn't available for customers (drop-shippers) who purchase products for the purpose of resale or use Amazon Prime to ship products to their customers or potential customers. Hence, you cannot use prime products for drop-shipping.
We recommend drop-shipping to only those stores which already sell on Amazon and can use their inventory to fulfill orders from WooCommerce.