kindles are difficult to filter.
Basic bypass - reset the machine. You find out AFTER if you check if the password has changed when the kid reset it.
Better filter bypass - when on 'silk', the kindle browser, you bring up chrome. and you're off and running.
Now I have Qustodio Free on my kindle. and I set it to shut down the the machine at off hours. I think I'm/ my kid is safe now.
But I may be mistaken.