DVL testing of blown flap for messerschmitt, dated December 1943 me-109s
First, the photo shows what looks like a pure test-bench configuration. The flap is full span, with no aileron for roll control. A large, static, probably electrically driven compressor supplies air through a bulky duct. Perhaps an operational fighter engine's compressor could provide enough air at takeoff. But the ducting and control doors would be bulky and, I'd expect heavy, even if they did not interfere with boost at altitude.
Second, what was the operational requirement? The Bf109's low-speed handling may not have been ideal. But, in 1943, it had been in service for six or so years. So surely handling was good enough for wartime?
Air entered the scoop below the fuselage and was accelerated along a duct by a fan driven from the rear of the engine. The duct was divided into three, one leading along each mainplane and one exiting beneath the fuselage. The amount of air entering each could be controlled with valves. The ducts meant the Me 109 S couldn't use the normal coolant radiators so an evaporative cooling system was used. This meant fitting a 44 gallon coolant tank behind the pilot, which messed up the aircraft's c.g. so the fuselage had to be lengthened. The air ducts also prevented the undercarriage from retracting properly, and this problem seems never to have been satisfactorily rectified - as least as far as the French subcontractors knew.
Date-wise, the work carried on in France until the Liberation, after which point there doesn't seem to have been any further work done on it in Germany either. Why did it carry on so long? I don't know. I just know that it did.