Dead bird in the chimney ?
I'll second that - dead something, somewhere.
I had a similar problem in a previous flat.
Seal the room. Seal your mouth & nostrils (I used a 'proper' paint sprayer's mask with filters) and give the room a thorough blast with a can of fly killer (Sorry - I don't remember which type I used, but it was readily available).
Close the door and leave the room unopened for at least an hour.
When you return, the corpses will have collected around wherever the flies are entering the room.
You've then to make the decision as to whether you need to rip out chimney breasts / floorboards, or whether further blasting with the toxins in the immediate area will suffice.
Edit - in one instance there was something dead under my floor, in another a bird had somehow jammed itself into the barge boards and expired there.