Only family founder can delete the family.
From mobile application, family founder has first to delete all other members and then delete his own account. See previous article on how you can delete a member.
From Web, go to « Family settings » by clicking on your name on the top right section and then edit family information. The family deletion button is accessible there.
The family will be permanently deleted along with all associated data. A message notifies the family founder that all family data will be permanently deleted.