Via Carol, if you ‘like’ the American Express Facebook page then you can take advantage of their “Link, Like, Love” promotion: link any Amex card and then you can register for a bunch of different offers including receiving a $40 statement credit for $100 Sheraton spend on the card by the end of August and a separate $40 statement credit for $100 Westin spend by the end of August.
There are a few others that may be useful depending on your interest, $5 back on $20 spend at Whole Foods or maybe there’s some non-zero chance of spending $25 at Outback Steakhouse by August 18.
I do see $15 off $50 at 1-800-Flowers, presumably you could do a $50 order with full mileage earning through one of the shopping portals, and all that Amex sees is that you’re spending $50, and you’ll get $15 back. While the offer does say “cannot be combined” it doesn’t seem as though that would mean couldn’t be combined with mileage or cash rebates through online shopping portals.
You can sign up for as many offers as you’d like (keep clicking more offers down at the bottom of the list). So sign up for all of them just in case you spend $10 at Dunkin’ Donuts or $75 at H&M.