How far are you from hatching? I would isolate that egg in its own container and clean them off of the rest of the eggs. Make sure your egg box is 100% air tight. Your cooler is obviously not totally air tight or the flys could not have got in.

Down here in FL I have problems with these flies for a couple of months every summer. Even when my snakes are totally clean they are around. Especially in the more humid baby tubs. This year I actually bought one of those UV bug zapper lights and that seemed to have helped a lot. Regardless, they only seem to be around for a couple months and then they are gone. I stopped seeing them at my place a couple weeks ago.