Response from the American Optometric Association:

Allison:
One cannot believe everything one gets from the Internet. Unless you are taking an excessive amount of photos each day, a camera flash should do no harm other than create a temporary afterimage, the dark spots that you have likely experienced when flashed. There is actually a vision screener called a Photoscreener that helps to determine whether a child has any eye problems by photographing the child and examining the reflex from the retina in the photo. One thing you may not know: We recommend that a child’s first eye examination (not just a pediatrician’s screening) occur at age 6 months. This will assure that any factors that could become a problem later in life are addressed and corrected early if necessary.

Not only is flash photography not a problem, the DOCTORS even use it in cases for retinal diagnoses.

I’m glad to know that my gut feeling on this was on target.