Suppose, for example, you want to fill the shadows on a face with an amount of light that makes the shadows one stop below the sunlit part of the face. To do that, the amount of light you need is dependent on the brightness of the sunlight on the face. It is purely a ratio of the main light (sun, in this case) to the amount of fill wanted.
The amount of flash power you need to achieve that amount of light on the face is dependent on flash-to-subject distance but is not dependent on camera settings. With the flash set up in this example, if you adjust your camera for f/16 and the sunlit parts of the faces are properly exposed, the filled parts will be exposed one stop below. Similarly, if you set aperture to f/11 and adjust shutter to properly expose the sunlit parts, leaving the flash set to the same settings and at the same distance, the filled part will still be one stop down.
So again, the amount of fill flash needed is dependent only on the brightness of the sun (or whatever the main light source is).
Now, when the flash is the main illumination, it's a wholly different case. Then there is direct relationship between camera settings and the amount of flash needed. But not for fill flash.