I placed an order on Amazon and I wanted to cancel it a few minutes later (wanted to reorder using the Amazon Store Card). You are allowed to cancel the order from the order details page, but probably since I chose Amazon Prime shipping option, the option to cancel the order vanished after a few minutes.
After trying different tricks for about an hour, I ended up canceling the order this way.
.) Google for 'Amazon Customer Care Phone Number'
.) I got the following link: http://www.amazon.com/gp/help/customer/display.html?ie=UTF8&nodeId=518316
.) Choose 'Your Orders', and choose the order you wish to cancel.
Try to describe the problem in some detail, and then click on 'Chat'. It will launch a live chat session with an Amazon associate and they can help you cancel your order.
Now, getting back to place the order again with a different card.
Update: the direct link seems to be this: http://www.amazon.com/gp/help/contact-us/general-questions.html