Same problem, I bought the 5700 XT from Amazon directly, verified it's shipped and sold by Amazon. No codes received, contacted Amazon support and this was there reply.
It makes no sense since they advertise the promotion on the actual product page. But as we are all slowly learning, Amazon support is impossible to deal with so it looks like I will need to return the card and order from another retailer.
Upon checking the details of the promotion and the eligibility criteria I see that the promotion is applicable only for few targeted customers.
We occasionally offer promotions to potential customers or to select existing customers, to encourage them to shop at Amazon.com.
The promotion you mentioned was offered by invitation only to a limited group of customers, and is valid only for the e-mail addresses to which it was sent. We regret that we cannot extend this offer to other customers.
In the meantime, you may wish to visit other areas of our website for great deals every day:
