Ambient (light) exposure is based on shutter speed and aperture.
Flash exposure is based on aperture and distance to subject.
Ignoring ISO sensitivity above as it's in common with both.
If you say set your flash manually to a constant output level (eg. 1/32), and take the same composed shot at 1/60s and 1/500s - and you're using flash as your sole source of light, the two images will not differ in exposure. Not one bit. Changing shutter speed as no effect on flash exposures - this may sound strange if you're used to ambient (non-flash) exposures where shutter speed is very much a factor.
If you're in darkness and relying solely on flash to illuminate the scene, don't be afraid to crank up that shutter speed if you need it to freeze the action.
BTW, the D70/s camera as is shipped is set up with 1/60s as the
minimum shutter speed in aperture/program/auto
mode. That means no matter the ambient reading, turning on the flash (SB800 or built-in) your shutter speed will be bumped up to 1/60s. This minimum setting can be changed from 1 second upto 1/125s in the custom functions menu, but any faster and you'll have to manually switch to shutter priority or manual
modes and select the appropriate shutter speed.
The D70/s's flash sync speed (maximum shutter speed when flash is used) is 1/500s. To exceed 1/500s - the camera needs to support Auto FP (focal plane)
mode. The D200 and D2 series Nikon SLR cameras supports this. To exceed 1/500s on a D70, you will need to use an external speedlight (eg. SB600/SB800) and 'retard' the flash exposure system by half chopping off the camera to flash communications. This can be done by masking the two frontmost contact points on the flash hotshoe connector.
I have tried this with an SB800 on my D70 and it seems to work without much negative effects. ie. still retains full (or close to full) iTTL flash metering capabilities (incl. balanced fill), all the way upto 1/8000s shutter speed, but the flash
mode 'defaults' to slow sync (ie. able to drop below the 1/60s or set minimum shutter speed if ambient exposure dictates).
However because this is not an officially documented feature, I suspect it shouldn't be used because of some dramatic ill effect it may have on your images, camera and/or flash unit under certain circumstances and I'll disclaim all responsibilities if you wish to try this - do so at your own risk.