nikon - Using flash with Aperture Priority or Shutter Priority gives me a white image - why?

When using the built in flash with Aperture Priority or Shutter Priority selected, I am getting a completely overexposed (white) image.

Now my understanding of AP and SP modes is that the camera manages the aperture or shutter speed to set the correct exposure, based on the selected aperture / shutter speed. I am shooting with an ISO setting of 100.

For example, when I'm shooting using the flash in low light, with AP mode selected + ISO:100, why does the camera not give a fast enough shutter speed to prevent this over exposure?

Clearly something major I'm doing wrong! Any help much appreciated.