I know some of you would say just pick up after him. However, we take him out to the dog run just before we leave for work in the morning we can't be there all day waiting for him to do his bio-break so can pick up and clean up. ...We get home and there is a total mess in the dog run.
Go outside with the dog and pick up after him immediately?
I don't think this is necessarily possible for the OP.
I have never faced this problem before, but u wonder if there is a way to deter the flies (perhaps a supplement that makes the "du-du" taste bad to flies). Otherwise, I would say that while you are home, during these "biobreaks" try and redirect the pup's attention with toys. Perhaps that will help the dog lose interest. Hopefully others will respond with more help.