You need to purchase a gift card (e-card works), this does not work if you top up your own balance. You can however redeem the gift card you purchase on your own account by emailing it to yourself and adding the token in your account. Use the link above and click the "Click to add coupon to your account"
You must have a US prime account
The $10 promotional credit is not delivered instantly, so it is unlikely you can use it on something today.
Make sure at the checkout stage of your $50 gift card purchase it says at the top "Important message, your first $50 card purchase qualifies you for an amazon.com credit. A $10 promotional code will be automatically applied to your account and emailed to you withou two(2) days after shipping."
Deal description from Amazon:
Today only, Prime members can get $10 in Amazon promotional credit by purchasing at least $50 in Amazon.com Gift Cards. Just click the yellow "Click to add the code to your account" button below, and add a qualifying gift card to your cart. This offer is valid today only, July 12, 2016, and while supplies last. Limit one per customer.
A $10 promotional credit will be applied to your account within two days after your qualifying gift card purchase ships. Credit is valid on items sold and shipped by Amazon.com and expires on August 27, 2016. For complete promotion terms and conditions, please scroll down on this page.
Original deal from Slickdeals
If anyone has feedback on the description (Such as the process not being clear) let me know! There's been a fair bit of confusing over on SlickDeals reading through the comments!