add my son's email account to my Xbox account

Are you wanting to add his email as an email used to sign into your account?

As long as his email is not currently a MS account you would be able to do that by going to account.microsoft.com/addassocid and add his account as an alias to your account that way he then can use his email address to sign into your account and you would
still be able to use your email address to sign into your account also.

If his email is already a MS account then you would not be able to do that.

So, he could use a gmail address?

Yes as long as he is not using it on another MS account

Yes, he can use sny email account as alias. Add it to your account and made it

primary for sign in to account

The problem with the suggested solutions about adding your son's email as a sign in alias are, that your son will get access to your actual Microsoft Account, meaning your Outlook.com Email, your OneDrive Cloud storage or whatever other Microsoft Account
services you use.

If you don't use these features, and you have a third party email (like Gmail, Yahoo Mail, or your own domain), and do not use Outlook.com, Hotmail.com or Live.com as your email address, you can have your son remove your email after he added his own email.

This will then delete the Microsoft Account part of your E-Mail address, and after your son made the switch, you can then create your Microsoft Account again, if needed.