Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Chicago Midway Airport to Fort Leonard Wood as you normally would.
Due to multiple factors, expect to potentially pay more when booking in August. For low rates, March can be a great choice for travel to Fort Leonard Wood. Flights to Fort Leonard Wood from Chicago Midway Airport in March are about $250 on average during March, but can be found for as low as $160.