My question is what shutter speed setting do I use when using the flash
unit.


You can use any shutter speed, up to the camera's maximum speed of 1/300 of
a second.

The Yashica-A was my first camera, which I was given at age 9, along with a
Sekonic "Brockway" exposure meter.

It has been awhile since I used it, and I do not recall if there was an "X"
synchronization setting. The camera came out circa 1958. Were there any
electronic flash units available then? I don't think I ever used a flash
unit with my camera--all my shots with it were taken in daylight.

The irony of this is that, even after I migrated to 35mm photography, I
typically used the 50mm normal lens for about 90 percent of my work (I shoot
landscapes, street scenes and buildings that are about to be demolished--my
little way of preserving the past). The 80mm normal lens on the "A" might
have been an impediment to some, but I could have gotten by with that camera
and lens for decades, and would have been quite happy with the results.
Even that non-coated lens yields more image quality than the best 35mm,
because of the greater film size.

It might not be the best choice for action photos, where automatic exposure
and faster film advance are real advantages, but for more static subjects it
remains a fine piece of equipment. Enjoy it!