Great question — answering as the UphillTech team:
This is directly from Amazon Associates, the short answer is no you cannot track Amazon sales as conversions in Google Analytics. The Amazon Associates reports will only reflect clicks that result in a session being created. This means the customer must click though your Associates link and the Amazon.com site must load. Many third party tracking methods will use impression tracking to count clicks. These reports will provide a higher number of clicks that would not represent a site visitor going to the Amazon.com site. Unfortunately, we do not have a way of integrating Amazon Associate sales into Google's Analytic tracking. However, I did want to thank you for taking the time to share your...
Full answer by Anagio: https://webmasters.stackexchange.com/a/38309 (CC BY-SA 3.0).
Need it done for your business? UphillTech.