While looking around on the AAA website I stumbled upon the Visa gift card landing page here. According to the details on the page from May 1st to Jun 30th you could get the Visa gift cards from AAA location without paying any purchase fees. The gift cards are issued by Metabank and they do come with a pin which means these cards can be loaded on to bluebird, serve and redbird. I think this is huge and you could possibly generate a lot of miles and points as there is no limit on how many cards you can purchase (confirmed by calling AAA although ymmv).
I will be heading to my local AAA store tomorrow to buy bunch of gift cards. Although I think this offer may be available only for the mid-Atlantic region but you can call your local AAA office and confirm. You can find the nearest AAA office by visiting this link. I will update the post with latest data points. Please share with other readers your experience purchasing gift cards from AAA.