【Updated 2022.10.3】The wine purchase made through a cashback portal link has already triggered the offer and was successfully reimbursed, so everyone can feel comfortable buying. 
AMEX currently has offers for Laithwaites and WSJ Wine. Spend $40 at Laithwaites and get $40 back, up to two times; spend $50 at WSJ Wine and get $50 back, one time. The offers are as follows:
Right now, purchases through TopCashback can also earn $31.5 cashback for each offer. If you do not yet have a TopCashback account, you can sign up through our referral link:
For a first order, Laithwaites offers 8 bottles of wine + 2 glasses for $49.99 plus tax. WSJ Wine offers 14 bottles of wine + 2 glasses for $69.99 + $19.99 shipping + tax. Unless you specifically need more wine right now, we recommend only doing the Laithwaites deal. Your cost is $53.50, with $40 back from AMEX and $31.50 back from TopCashback, which makes it effectively 8 free bottles of wine plus an $18 profit. Cashback tracked in about two hours: 
After the wine arrives, remember to skip the subscription until the cashback posts, and be sure to cancel the subscription afterward so you do not get charged later.