Using Magento CE and will be integrating both Amazon Payments for checkout and Amazon Fullfilment.
Amazon provides their 'Pay with Amazon' Magento extension, and there are a few extension out there for fullfilment (including inventory sync).
What I'm having a hard time finding any info on, is regarding how to handle Amazon Prime. Both the display of Prime eligible on the eligible products and ensuring that prime customers receive the appropriate shipping fullfilment time (and show that on the shopping cart, and pass the data through to Amazon appropriately).
Neither the Amazon Payment extension, or the few Amazon fulfilment extension found mention the management of Prime products and customers (and not getting responses from inquiries).
Any information towards the above would be extremely helpful in helping to determine the level of effort to implement (as that needs to be determined before the integration project is approved).