Assuming you are on a single itinerary (given that you have mentioned codeshare flights), your luggage will be tagged to your final destination, Cincinnati.
What this means in practice is that you will not need to collect and recheck your luggage in London. However, you will need to collect it and recheck in Chicago.
When you first arrive in the US, you will be required to clear customs. This requires you to walk through the declaration lane with all of your luggage.
Immediately following immigration to the US, collect your luggage from the belt, walk through customs, then after customs, you will find a desk where you can onward check your luggage for the final leg of your flight.