To dropship via Amazon, you need to follow Amazon's policies and terms.
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 can't use prime products for dropshipping.
We recommend drop-shipping to only those stores which already sell on Amazon and can use their inventory to fulfill orders from Shopify.