Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Flagstaff to Laughlin as you normally would.
Due to multiple factors, expect to potentially pay more when booking in June. For low rates, August can be a great choice for travel to Laughlin. Flights to Laughlin from Flagstaff in August are about $538 on average during August, but can be found for as low as $159.