Gold bought on Apple covers one account
A Gold Membership bought in the ChessKid app on iPhone or iPad applies to the one ChessKid account that was logged in. The app offers Monthly, Quarterly, and Yearly. It does not sell a plan for 1 kid, 2 kids, or more.
The same Apple ID also can't buy Gold for a second ChessKid account while the first subscription is still active. The app shows: "Cannot buy subscription. This Apple ID has been used to buy Gold for account [username]."
If you bought the Apple Gold on your adult account
Buying a plan on the ChessKid website replaces that Apple plan. It does not add a second plan on top.
Log in to your adult account on ChessKid.
Open the Membership page and select the period you want.
Under Kids, use + to set how many kids the plan should cover, then pay by card or PayPal.
Go to Manage, then Kids, and click the green badge next to each kid to give them Gold.
ChessKid ends the Apple plan on your account as soon as the website plan starts. The unused part of ChessKid's price for that plan is taken off the new purchase. This is not a refund from Apple, and it may not match what Apple charged you.
Cancel the subscription in Apple too. ChessKid can't stop Apple billing you, so Apple keeps charging until you cancel there.
Check out this article to learn how to manage your Apple Gold membership purchase: How to cancel, change, or get a refund for a Gold Membership purchased through Apple
If the Apple Gold is on a kid's account
That plan belongs to the kid. A purchase on your adult account does not replace it.
Buy the website plan from your adult account, using the steps above.
Assign Gold from Manage > Kids. The kid who already has Gold keeps it until their Apple plan ends, and the green badge appears for them only after that.
Cancel the Apple subscription with the Apple ID that bought it, using the article linked above. Until then, Apple keeps charging.