Can I link my Pokémon Trainer Club account to Niantic Kids or Google accounts or transfer progress?
There is no account linking or progress transfer functionality between Pokémon Trainer Club accounts, Google accounts, and Niantic Kids accounts.
For information regarding Niantic Kids account features, functionality, and support please visit the Niantic Kids Support website at: https://niantic.helpshift.com/a/pokemon-go/?p=web&l=en&s=safety-and-security&f=niantic-kids-support.
Note: the link takes you to a website that is not created or maintained by the Pokémon Company International.
Source: Pokémon Support