My problem with the Free Time app was that it made me enter a my pin code at power on and after the screen saver came on. I did a search of Kindle Fire Help and found this entry:
Turn On or Off Your Lock Screen Password or PIN
Following the instructions, I was able to disable the PIN code entry.
If you are like me and just want to disable this "feature", follow the steps above to remove the Free Time from the carousel and follow the steps in the help article. (Since I don't have kids, the Free Time app is useless!)