[JoeD]

I don't think there is, although I wish you could disable on click purchases on the device or at least activate an option to require a password/pin to buy.

I'd suggest making a new account just for your kids devices (put both their devices on the same account though so they can read the same books). Don't put a CC on the account and instead purchase gift cards using your account and activate the gift card on theirs. That way they can still buy books as needed, but won't run up a huge bill by mistake and you don't have to worry about them reading books you've bought that may not be suitable.

Also, you can make the account using an email address under your control, so you can keep an eye on any free book purchases made too just in case they happen to buy something you deem unsuitable.

Trust is fine, and you're still going to be trusting them to not buy inappropriate freebies (even though you can monitor the email address just in case), but sometimes it's not obvious a book isn't for them and it'd be all too easy for them to see a cover/description that looks appealing that turns out to not be suitable.

Other advantage to the 2nd account is your recommendations and their recommendations will likely be wildly different.