Amex Platinum card does not give you any baggage allowance. Do you mean the Delta Skymiles Platinum American Express card? This is nominally only a first bag free benefit and not a +1 benefit. There is an exception for Silver Medallions who get two free bags free on domestic flights with the card, but Gold's and higher do not get any additional allowance with the card above their normal allowances.

https://www.delta.com/content/www/en...p/checked.html

"Silver Medallions who hold a Delta SkyMiles Credit Card from American Express will receive a second bag free (up to two free bags at 70 pounds or 32KG each) for travel within the U.S. and Canada."