We are unable to look up an item using the RN #. However, an associate or manager can try to look up the item on the computer (not the register) using the brand and description of the coat. Also, if you check the inside of the coat there may be a tag attached to the left side that may have the UPC on it which would be a really long number, usually starting with a 4. However, this may be where you got the RN number from, which in that case I would just take it up to your kohl's and have them do a look up. I have to do things like this everyday since I am a Kohl's Customer Service employee. From there, they can let you exchange it for something of comparable original price (another coat perhaps? or anything of your liking) or if you purchased it with a credit/debit/kohls card they can do a look up and give you a refund back to your card (or cash if it was a debit card) for the amount you purchased it for.
The only other option if you didnt purchase it with a card and you dont have a receipt is to give you a KMRC (merchandise credit) which would be for the lowest price it has been in the system. I hope this helps you somewhat. But I'm sure something will get done for you if you take it into your store :)