While Zendrop does not have a direct integration with Amazon, it is possible to pull orders from Amazon into Shopify using a number of different Shopify App Store apps.
The app that we recommend is Amazon by Codisto.
IMPORTANT NOTE: Zendrop has not tested the functionality of this app nor has any affiliation with the developers of Amazon by Codisto. However, Zendrop sellers have had success using this app with Shopify and Zendrop.
You will need to either have an Amazon Seller account or create one when setting up the app.
The Amazon by Codisto app pulls orders from Amazon into Shopify which then pulls the orders from Shopify into Zendrop where you can fulfill them like you would any other order.