You could do something like this via Flow. You could grab the parent and child records, and then duplicate/clone them manually inside your Flow.
Just pass the (parent) ID into the Flow --> grab the child records for records with parent ID = to the ID passed in. And now create the cloned records.
Depending on how many records you plan on having... if you plan to hit over 20~ records then you might want to not use a standard Record Create because you'll potentially loop through more than the allotted 50 lookup/creates that you get in your Flow. In that case, you would want to use a Fast Lookup/Create and use the assignments to setup it correctly.