Get an IR camera. You should be able to find cracks/leaks/whatever real easy. Unfortunately IR cameras aren't cheap, so perhaps you can call a HERS guy to come over with one and pay him $100 for his trouble.
If that fails, I suppose you could fill your house up with a smoke machine and attach a blower door (you'd need the help of a HERS guy again)... or just use a smoke pencil.
Like others have said, there's probably a dead thing somewhere. However, depending on the fly type, they could be breeding in very dirty water or in pretty much any organic matter. For example, some will breed in rotting vegetation, some will eat wool or fleece if they have too. So looking for pretty much anything out of the way that could be rotting. You may not find it though - attics, basements, even in the walls if a rat died in there or something.
The life cycle of flies is often very temperature dependent - it slows down when it is cold and speeds up when warm. Some of the common flies found in houses can go from egg to adult in about a day in ideal conditions, so even if you kill them or let them out, this is probably how they are replenishing - new ones are hatching.
I looked up the breeding time and so on a while back, when this happened to my Mum - all these flies showed up in the lobby to the house one morning, on the ceiling. It was kind of creepy. We cleaned out the room, and couldn't find any obvious points of entry from the ceiling or floor, so you're not the only one!
What do your flies look like? Different ones eat different things and have different habits.
This interesting looking chart describes them and gives their "favourite foods" as well.
http://www.jfoakes.com/fly_identification_chart.htm
This site gives many many pictures of flies. If you click on the headers above each row of pictures, you get more pictures of flies in that subgroup, so you can keep getting more and more specific pictures and ID. Not recommended if you are grossed out by fly pictures.
http://bugguide.net/node/view/55/bgpage
Best Answer
It's hard to give accurate advice without more information about the building. They've got to get in from the outside, but they can get into your room though an attic, crawlspace, etc. Go outside and look for openings. A common place is where the electrical service enters the house through an attic. If you go out in the middle of the day, you should be able to see them flying around.
The house I grew up in had a HUGE bee infestation in the attic. They got in through soffit vents. Every once and a while a couple of bees would come into my room through openings around the A/C register. No one figured out that they were coming in from the attic until honey started dripping through the drywall ceiling (my mom had first blamed me for spilling something sticky on the carpet). They had to go in and out to feed, and we did notice them outside, but we did not think they had actually nested in our house. They were much more evident outside than inside.
So, with this experience, I say take the time to observe them from the outside to determine where they are coming into the building structure, then search for nests.