I had a lot of very small flies in my house recently, they were driving me mad. We really couldn't work out where they were coming from but eventually found a couple of rather mouldy potatos that had fallen down the back of a shelf in the kitchen.
If they are the very small house flies then they are attracted to fruit, vegetables and fermenting liquids. They seemed to congregate around wine bottles that had been kept for recycling (but not rinsed out, oops!).
Before we found the source I became obsessed with setting tempting wine/jam based traps and, when a few gathered, blasting them with fly spray....