Make sure the correct account is linked then head to https://www.bungie.net/7/en/Codes/Partners and hit refresh. It should then appear on the list, if it does then give it a few minutes then restart D2 and recheck your collections. If it doesn't then you'll want to check with Twitch support to see if there is any issues and refresh again after a short while. If the item is the ship or some other non-emblem item then check the special deliveries kiosk once its displayed on the partner reward page.