[Update 2021.12] Some users can now see a donation offer: donate $1 and earn 40 AA miles. Combined with this 5x promotion, that means a $100 donation can earn 24,000 AA miles (worth about $360). So if you need AA miles, this is effectively an indirect way to buy miles at a cost of just 0.416c/p, far below our 1.5c/p valuation of AA miles.
That said, please still be cautious. Although FM contacted AA and confirmed that this offer is valid, I still would not recommend going too big, because if something that seems too good to be true ends up not being honored, it could be a real hassle.
AA SimplyMiles has a new promo: through December 27, all offers that earn miles will receive 5x rewards. I took a look and some offers from AT&T, CVS, and Best Buy are pretty decent. You just need to add your credit card to the program and make the purchase with that card; there is no need to go through a specific shopping portal or website.
Based on readers' previous experience, this 5x bonus applies directly to the miles earned from the offer. For example, at CVS, spend $45 and earn 1,500 miles; this promo would also add another 7,500 miles, which is very strong. If you see a merchant you need, remember to link your credit card and use it.