I saw this article on lifehacker about Epic!, and thought there may be parents here on mobileread interested in it. I'm sure there are other services like this, but lifehacker describes it as "netfilx for children's books". Their app is available for apple, android, and kindle fire. No ads or in-app purchases, and age appropriate books for children 12 and under. It's a subscription service.
https://lifehacker.com/epic-gives-ki...ary-1792021055
https://www.getepic.com