There is an ordering API for the Amazon Marketplace . If you are a seller and want to know what orders have been placed for you, this is the way to go.
If you are a customer and want to check the orders placed by you, the best option I know is a screen scraper (maybe an API that I am not familiar with). I have used the HTML Agility Pack in the past for this type of thing. It allows you to enter the website, and then helps in analyzing the page you are interested in, which may be the order page.
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