The Program mode setting is at one end of the Tv dial (shutter speed), and the instructions say the lens aperture ring has to be locked in the Auto position. So neither shutter speed nor aperture can be set. As the A-1 was the first camera with a Program mode and the 199A flash was dedicated to it, it's strange that flash and Program aren't mentioned anywhere.
I can of course use aperture priority or manual as I've always done, but I assumed the Program mode and the dedicated flash must "talk" to one another. I've almost finished a film with flash in Program so it will be interesting to see the results. The closest thing to an answer in the instruction manual states the flash will work automatically at any setting on the aperture or shutter priority dials. As Program is at one end of the shutter dial, maybe it's okay, but if I can't set the aperture, who knows?