To access your ChessKid gold membership on the website, you just need to log in with the same username and password as you would on your Apple device.
If you're unsure of your username, you can recover it by logging into the app (on the device where the purchase was made) with any username (or create a new username on the app) and going through the motions of purchasing a membership without actually purchasing one.
When you do this, it should give you a pop-up with the ChessKid username that is linked to your Apple ID. This will give you the username connected to the gold account purchase.
Once you have found the username on your device, if you need your password reset you can EMAIL US and we'll take care of that for you.