You can get these offers through twitter, facebook, and foursquare also if your Amex account isn't showing these. Sometimes there are offers on one site that are not on another.
https://sync.americanexpress.com/
The twitter and foursquare ones can be a bit confusing if you are not familiar with them, so I suggest using Facebook.
My Macy's card is also an amex. They don't have offers on the macy account, but I linked that card to facebook amex page and am able to get offers through there.
Almost all of the offers allow gift card purchases (but not e-gift cards). I have bought gift cards at Lands End, Kohls,
Amazon, Costco, West Elm, J. Crew, and Sprouts. All worked.