OMG, Will, that's disgusting. But I also suspect it could be the answer. Yuuuccckk!
There could very easily be a dead mouse in the garage-- and the door to the garage is not tight. And it's right next to the kitchen, which is where the flies are, except for the ones that are trying to escape outside, and have gone to the sun porch. Where I have been pretty successful at shooing them out the door -- they land on the screen, and every half hour or so, I open the screen door and shoo three or four more flies out (this morning, it was six at a time).
Two weeks?? Maybe I can put tape around the edge of the garage door into the kitchen. I'm sure there must also be entries through the walls, but if the dead mouse is in the garage, that would at least slow them down.
Possible of course that the dead critter is in the walls.
Still, I feel a lot better having an explanation that does not involve food being infested.
Dmkly, I've been thinking about that sticky flypaper. If they persist, I will invest in some. Way better than using chemicals, although I will have to get my husband to remove it, because it is sooooo grossss.