Custom field in discourseconnect

If you have created those fields via the Admin → Customize → User Fields, you need to pass it as

$parameters =  array(
            'nonce'       => $nonce,
            'external_id' => 'jay',
            'email'       => 'bugsbunny@betaclub.org',
            'username'    => 'bugsbunny@betaclub.org',
            'name'        => 'Bugs Bunny',
            'add_groups'  => 'state_sponsors',
            'custom.user_field_1' => 'Pro',
            'custom.user_field_2' => 'FL',
        );

The field names aren’t the name you set on the UI, but numbered fields named user_field_NUMBER.