Shutter speed doesn't have anything to do with exposure in flash photography (except for fill flash, of course.) It is simply a way to synchronize the shutter and flash unit. The actual exposure time is very short and is governed by the duration of the flash itself. It is the aperture that adjusts exposure in flash photography.
TTL flash exposure automation actually reads the amount of light hitting the sensor and shuts off the flash as soon as enough light has reached the sensor. In other words use the aperture to control things like depth of field and let the flash automation worry about the exposure. If you want a higher or lower flash synch speed, then use manual mode.
As a matter of advice, I recommend you stay away from shutter and aperture priority. They are throwbacks to the early days of exposure automated cameras. The P mode on the nikon does every thing these two modes do and does it faster and easier. You can cycle through the various combinations of aperture and shutter speed that result in the same exposure by turning the little command wheel. So you can adjust for aperture or shutter speed with one mode and the little wheel. I'm surprised these older modes are still included in modern cameras. You shouldn't need anything except P or program mode for automated expoure and M for manual exposure. I understand why they provide the A or auto mode for those that want point and shoot photography. A mode doesn't do anything the P mode doesn't do just as well either. The other modes just complicate the issue.