Our dog loves to chase flies too. But when a 110 # dog decides to chase a fly as you are driving down I-5 it makes for a bumpy, shaky, bit scary rideOddly enough, my dogs are great for flies. The younger one has a super long tongue and picks them off when they are crawling up the window. Of course that does lead to lots of dog art on the window pane, but it washes off easy enough. The older dog is really good at snapping them out of mid-air when they fly near him.
You could possibly put a fly trap near by but out of the way..... These work really well. If you put meat products in them, you will also catch yellow jackets... Quick and Easy Homemade Fly Trap (REALLY works!)