There is no Access (view) Level for owners
Nevertheless it is possible to display a field to items owner only:
-- for item view (file item.php)
$curr_user= JFactory::getUser();
if ($curr_user->id == $this->item->created_by) {
FlexicontentFields::getFieldDisplay($this->item, 'fieldname');
echo $this->item->fields['fieldname']->label .": ";
echo $this->item->fields['fieldname']->display;
}
-- for category view (file category_items.php) use either $items[$i] or $item instead of $this->item