Where could all these flies be coming from?
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