What sort of flies have you got? Blue bottle/ house/ little tiddly ones?
I had a bit of an onslaught of tiny flies this year because of having trays of stuff growing on the windowsills. I bought some fly window stickers in Homebase and they seem to have done the trick although I have a lot of tiny corpses stuck on them now. Might have to buy some new ones. Should work for bigger flies too.
I don't seem to have a problem with flies around the c & c (touch wood) so not sure what to suggest. I have the same routine as you for cleaning/ poop scooping. The only thing that is different is that I use washable incontinence pads instead of towels. Mainly because I found the towels got smelly very quickly and they took to long to dry on the airer indoors.
Hope you can get your problem sorted out. I hate flies too.