How do I get the administrator to automatically flag?
FlagServiceInterface::flag takes an $account argument:

The account of the user flagging the entity. If not given, the current user is used.

So for example:
$flag_id = 'moderate_node';
$flag_service = \Drupal::service('flag');
$flag = $flag_service-&gt;getFlagById($flag_id);
$account = \Drupal\user\Entity\User::load(1);
$flag_service-&gt;flag($flag, $node, $account);