Keep the catfood and the cats indoors. It's safer for the cats and won't contribute to the fly problem. Flies are attracted to garbage and waste material. Have a good fitting lid on your garbage can, pick up fallen fruit and veggies from the garden, scoop any poop from cats or dogs. You can use fly traps and fly strips. Chemical sprays will cause more problems than solve because they are indiscriminate and will kill any predators that might be helping you out by eating some of the flies.