You cannot have purchased gift cards through this account in the past or it won't work. Here are the terms and conditions:
From the Terms:
In order to qualify for the promotional credit, you must: (1) be a paid or trial member of Amazon Prime (as of the day prior to your purchase of the gift cards); (2) be making your first purchase of Amazon Gift Cards with this account; (3) purchase at least $45 in select holiday Amazon.com Gift Card ("GC") multi-packs between November 1, 2014 and November 15, 2014, 11:59 PM (PT); and (4) enter the promotional code "HOLIDAYGCS" in the "Gift Cards & Promotional Codes" box when you check out.
There appear to be some bugs with this code, though. After reading this thread, I was worried mine didn't go through as it didn't show up on my invoice so I called. I was told that once they process the purchase I will receive the $10 credit in my account and an email verification. The guy told me it showed up on their records but it still makes me a tad nervous that I have no confirmation at this point.
ETA: I am a trial Prime member and the guy on the phone first told me I didn't qualify, but then when I read him the above terms and conditions, he said, "Oh yes, there it is." Not too reassuring. Anyway, if you're getting this with a trial membership, be aware that you can't use this promo the same day you sign up. You have to wait at least a day to order.