Hiya,
FusionAuth provides the APIs and data entities, but you have to code the flow. This is because there are multiple choices for parental consent.
Again, still working on documentation, but basically, when the child registers, you'll need to make sure they have a parentEmail attribute associated with the user object. FusionAuth will send one of two email templates based on whether the parent has an account or not.
Then you have to have the parent grant consent, which means building a form that they can check a consent box in, and you then record that consent using the Consent API. If the consent is a COPPA email plus consent, FusionAuth will send a second email based on the tenant settings (make sure you use version 1.18+ because of this issue: https://github.com/FusionAuth/fusionauth-issues/issues/724 ).
When a child is signed in, you can get any consents they have been granted, so your application can prohibit any functionality that needs parental consent.
Here's a sample app for the consent granting that may be helpful: https://github.com/FusionAuth/fusionauth-example-family