I was told by multiple reps that it can be used online, but I don't see where to input it, so I have to assume that they don't know what they're talking about (what a surprise ).
Feel free to PM an offer.
Quote from their fine print upon clicking 'gift cards':
"Using Your Advance Auto Parts Gift Cards
We currently cannot accept Advance Auto Parts gift cards for online purchases. We plan to add this payment method in the near future. In the meantime, you can use your gift card for purchases at any store."
Also, from the same place:
"Purchase Advance Auto Parts Gift Cards Online
Note: You will be redirected to a third-party site hosted by one of our trusted partners. To purchase an Advance Auto Parts Gift Card on this site, please create a separate account."
So buying GCs on line from them probably won't work for the Amex offer.