I've managed to solve this headache. I was experiencing the same issues as reported above.
- Your child needs their own email
- Add them to the household account
- They'll receive an email to accept
- Take that link in the email and copy/paste it into a new browser session (incognito or new chrome account) and open it from there. Fill in the form and it worked for me, with the confirmation page after providing the membership number for your child.
This last part was tripping me up. You need to activate this link outside of your BA account. I think it's conflicting when you're logged in or the cache in the browser, which gives the age restriction message and stops that form working.
BA's website does a poor job of explaining of whether children can even earn avios, let alone how to actually set it up. I nearly filled in a PDF form for a "nominee" ownership at one stage. It's so easy to provide clear instructions, anyway. Hope that helps someone.