Panther chameleon females can lay anywhere from 10-40 eggs per clutch. The number of eggs depends on the food and nutrient consumption during the period of development while the eggs are in their womb(gravid).
How many are there?Are these flies able to fit through the mesh/screen of your enclosure? It can be that if you have flies in your house some may have just flew in your cage. Or there is the possibility they are reproducing in the soil of your live plants.
Try sending Dooley1 a PM. He is very experienced with carpets and can point you in the right direction. If you do end up getting a carpet I would definitely recommend buying one from him as well.