All you need to do is link your Amex Membership Reward-earning credit card to your Amazon account. Then just activate the discount through the promotional page, add items shipped and sold by Amazon to your cart, then apply a single Membership Rewards point to your purchase to unlock these savings.
Get up to 40% Off Amazon by Using Amex Points! - Thrifty Traveler
thriftytraveler.com > deals > points > amazon-amex-promo
You can redeem Membership Rewards points to buy items on Amazon through the Amazon Shop with Points program. Points are worth 0.7 cent each this way, meaning that if you have 10,000 points, you can exchange them for $70 worth of Amazon merchandise. There's no minimum redemption amount.
Using AmEx Membership Rewards at Amazon Is a Poor Value - NerdWallet
www.nerdwallet.com > article > credit-cards > you-can-spend-amex-memb...
How to get 40% off by redeeming one Amex point
1. Check here to see if you have a targeted offer.
2. Activate the offer in your Amazon account.
3. Load up your cart with eligible items sold by Amazon instead of by third parties (yes, most gift cards count)
Save up to $40 on Amazon using just one Amex point (Targeted) thepointsguy.com > news > amazon-amex-membership-rewards-discount
These deals are targeted, so they won't work for everyone. If you aren't targeted, check the bottom of this post for some tips you can try to trigger the offers on your Amazon account.
Save Up to 40% on Amazon Purchases By Using Just 1 Point
awardwallet.com > blog > save-on-amazon-purchases-by-using-one-point