I get the impression that the screw slot is too small to use a turnscrew. The judicious application of a knife edge file will open that screw slot enough to use nearly any turnscrew. The slot will be tapered, as were the originals. Both modern screwdrivers, and/or HC tapered turnscrews work equally well on tapered screw slots.
And, as Birddog6 suggests, rework the top flat of the flint to make it hold better.
J.D.