I have set up parental controls on my neice's kindle. I found this website which gives step by step instructions on how to do that. If you set up those controls it will ask for a password whenever the child tries to access something that the parents have blocked. That way the parents have control over what the child puts on their kindle and can look at.

You can also set up maximum times if you wish for use of apps etc. through kindle freetime so for example, you can set that the child can only play games for 1 hour per day if that is a rule you have.