Instagram has a "Help Centre", within this is tips for parents which will give everything from the basics around Instagram to "How do I get an image of my child removed?"
Have a clear rule about clearing history
Monitor what accounts they’ve searched
Monitor what Hashtags they’ve searched or clicked on
Check their Explore feed, it shows posts based on your kids' history.
You can log into their account on your phone and easily switch between accounts.
Even if account is private using a hashtag makes the post public
Teach them to never use hashtags.