How to output values from a loop into a javascript array

This is not really a WordPress question.
However you probably need the implode php function, using a comma as glue.

foreach( $fields as $field ) {
  $value = get_field( $field['name'], 'user_'. $author_id );
  if(!empty($value)) {
    if ($value) {
      $v = implode(',', $value);
    }
  }
}