Talk

Yes you can as my 2 kids have theirs linked to mine. You can have quite a few devices linked to one account.

Thank you dementedpixie

Setting it up now.
Is there a way that one child doesn't see the other child's profile and books?

Not that I know of if both are on your account (essentially, Amazon assumes all the readers are you on multiple devices)

There are family accounts

When you buy a kindle book via Amazon website or the app then it asks you which device to send it to so it's not sent to all of them automatically. If you buy it from the actual kindle then I assume it is just sent to that individual device

Oh yes, pixie is right. Use amazon to push books out not the devices to pull books in.

You can then set controls on the individual kindle so it can't download things. Otherwise all the items you buy are available in the archive.

It's very very very poorly designed and clearly not tested by real users, but it can be done.
By the way, you can get a zillion ebooks for free from the library. I haven't purchased a book in years for me or the kids. Just check it out online and distribute to me or the kids' paperwhites.

If it is a new paperwhite it will have Kindle for kids settings. You can set up an account for each of them on your account and then you manage which books they are allowed access to. You need to enable it on their kindles as well.

Kindle for Kids is fantastic. I've linked my child's to my account and it then removes internet access without inputting the parental control password. So they can't browse or buy new books independently. It tracks their progress, sets daily reading goals and other achievements. My DC aged 9 loves it, it has turned them from a reluctant reader into one who asked for vouchers to spend on e-books for Christmas.