adding xbox live to xbox 360 own membership

Hello,

The Xbox One only requires one active gold membership for that console. Anyone that then signs into that console will have their own gold membership. It's not possible to merge these accounts if that's what you're inquiring about. Each account will continue
to be it's own separate entity with it's own gamerscore, saves, etc. You just won't have to pay for their Xbox LIVE Gold memberships if they wish to exclusively play on the Xbox One console and not go back to their Xbox 360.

If anyone wishes to use Xbox LIVE on their Xbox 360 console they will need a gold membership for the account that wishes to play online. The gold sharing feature is only available for the Xbox One.

He dosent have a xbox live account its family share so there's only one subscription

Now I'm a bit confused.

What exactly do you mean by "kid profile thing on your account" then?

Do you have an adult Microsoft Account, and is the kid added to
https://account.microsoft.com/family with their own child/kid account, or what do you mean exactly with the "kid profile thing"?

Ideally, each family member has their own Microsoft Account and Gamertag, so each person can save their own gaming progress and doesn't unlock achievements for someone else.

The family sharing is done on the Xbox One console. One person that owns a Gold membership can share that membership to one "Home Console", and everyone playing on that console can benefit from the Gold membership and the games that person purchased.

The Xbox 360 does not have the concept of the Home Console sharing. So if your kid is supposed to play online Multiplayer on the Xbox 360 (a real Xbox 360 console, not an emulated Xbox 360 game via Xbox One backwards compatibility), each account playing
on a Xbox 360 would need a separate Gold membership.

Sign in to Xbox LIVE with the account for which you want to use the prepaid code.

Press the Guide button on the controller.

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Go to Games & Apps and select Redeem Code.

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Enter the 25-character prepaid code and select Done.

When prompted, click Yes to confirm the redemption.

Here is what happens to your account when you redeem different types of prepaid codes:

Xbox 360 Entertainment For All Plan: You cannot “stack” or combine prepaid subscriptions during the life of the contract.

Xbox LIVE Gold Membership: An Xbox LIVE Gold Membership is added to your account, or an existing membership is extended.

Microsoft Points: Microsoft Points are added to your account.

Xbox LIVE Marketplace content: The content is added to your account and begins downloading.

Hello,

The Home Gold features are specifically for the Xbox One, they do not do anything for the Xbox 360. If your son wishes to use his Xbox 360 and play online he would need his own Xbox LIVE Gold membership. As far as the Home Gold is concerned anyone on that Xbox
One that decides to play on it with their gamertag will have a gold membership automatically as your account has a gold membership, it would be shared with the whole console.

That is not entirely true. Multiple accounts cannot share one Xbox Live membership. For each account to have it's own friends list and whatnot, they must each have their own Xbox Live membership.