No, Senator Herb Kohl does not own Kohl's Department Stores.
The store is owned by the Kohls Corporation which is a publicly
traded company. You can view the current list of owners on Yahoo
Finance here:
http://finance.yahoo.com/q/mh?s=KSS+Major+Holders.
The Kohl family sold their store back in 1979.
LOLing at this because my great uncle is Senator Herb Kohl