I contacted Kohl's and this is the response I got about using competitor/manufactured coupons.
Thank you for contacting regarding our policy on the use of competitor and/or manufacturer coupons. I understand your concern and would be happy to clarify this for you.
The decision to accept a manufacturer's or competitor's coupon is made by each individual store. To find out whether these types of coupons are accepted at your local Kohl's, please contact the store's Customer Service Department.