Well I have a new born. 5 weeks he is now. I have used flash and there was no screaming or crying, in fact there was hardly any indication that he noticed. Which is the same as with my other son, from what I remember when he was a new born. Now, that is bounced flashed and I was still using 400/800 film, f/2.8 so it is fairly gentle. I mean think about it, if you take a baby to a studio for photos, what do they use? Flash, strobes, big lights. If you think about it, daylight is f/16 at 1/125 with ISO 100 film, babies have to cope with it too. Anyway, each baby is different so I can't speak for every one of them.
In any case, flash done right is great. Fast film and wide open done right is also great. The one thing that is not great, a flash on the camera and blasting away straight to the subject. In general, when I use flash I either bounce it off a large wall or I use it off camera, I bought a pair of PocketWizard triggers and they are great. Small, reasonably priced, reliable and work with any camera. I stick one on the camera, hook the other on to the SB80DX and off we go.