Its fairly hard to install other ROMs on Fire tablets. But its very easy to install a different launcher and the Google Play store to make it look like a normal android tablet.
And that launcher would/should have lock-down features.
Problem is, it runs as slow as a dog on the 7/8 HD. Nevermind the basic model. They are basically trash.
That said, you know you can still add apps to the kids zone on the Fire tablet that aren't part of the subscription service, yes? You install them from the Amazon Android store on your profile, then add them to your kid's profile. The major issue here is that many "free" apps on the google play store are not free on the Amazon version. You can side-load, but you cannot add side-loaded apps to the Amazon Kid's profile.
They're not daft, they don't give these tablets away for pennies to make a long-term loss