Hi Walter Probably not. "Flat" roofs are not really flat, but have a shallow pitch, usually to a corner where there is a water collector to channel rainwater off the roof. I've seen this done a number of ways...on small houses often the original builder put 2 extra 2X4's on one top plate to give a 3" rise to one side of the roof.
The problems of trying to do what you are asking are many. Once you enclose the upstairs living space, you will have a thick coat of old tar under the floor, the odors of which will constantly fill the attic space. Trying to cut in a stairwell by working around the existing tar and paper will be a giant pain and your 2X4 sleepers will not be perfectly flat, as the tar coating itself is not flat.
No....I'd go through the work of pulling up the old roof. I know, this is laborious and messy, but IMHO, its worth it to get a professional looking job in the end.