Best answer as chosen by user Persistent_Dad: Not a native feature.

On the Kindle Fire you see Amazon setup parental controls with such features. I see you asked for an app but I didn't search for you. In the App store, look for PARENTAL CONTROLS.

I'm unsure why you would need to root the device. You may have to change that setting about installing 3rd party apps and I'm encountering folk that call that rooting (it's not.)