To share Amazon's Netflix competitor with someone else, you have to set up 1-Click, an aptly-named Amazon payment option which allows you to buy things with only one click of your mouse. After you click the button, the product is charged to the card and shipped to the address that's associated with 1-Click.
You can only have one card and one address associated with 1-Click, though the person you're sharing with can still charge products to different cards and ship them to different addresses