Any "flat" roof can be a prescription for trouble -- especially if it is nearly flat as opposed to having, say, a pitch of one or two inches for every 12 inches of run.
That said, I can't really get a mental picture from your note as to whether the flat section abuts any sidewalls of the house. If they do, the flashing between the flat section and the sidewalls could be the problem.
Another potential problem with a fairly flat roof is often at the edge. If the overhang isn't sufficient enough, or if the drip-edge details aren't carefully attended to, water clears the edge of the roof too slowly and wicks itself back up under the edge of the roof, along rafters and roofing boards -- and eventually into your living space. (This latter action describes the leaks in a sunporch in my summer place in Maine. Some summer I've got to fix it!)
I hope this helps, Ken Holmes email@example.com