Without light, objects cannot be seen, so some level of light is
necessary for display.  How much light and for how long is the question.

Consider the amount of energy released with each flash of a modern
"snapshot" camera.  The energy comes from a small battery (which lasts
hundreds of flashes) and thus the energy released in each flash is
absolutely minimal-especially when compared with sunlight or even low
room lighting.

And since the inverse square law applies, the distance between the light
source and the object remains important.  At two meters 1/4 the energy
strikes the object than at one meter, at three meters 1/9th, at 4 meters
1/16th and so forth.

Plus objects in cases or behind glass are further protected because some
light from photo flashes is reflected off the glass (especially if the
light strikes the glass at an angle) and light can also be absorbed
(usually very little however) and certain wavelengths of light can be
blocked by the glass if the glass is designed to do such.

A flash at four or five yards puts very, very little energy on an object
and has very little effect, if any.

Museum folks outlaw flash photos because they:

1.   Don't like the flashes, as suggested by others on Museum-L.
2.   Don't want folks to take pictures and use them for commercial
purposes.
3.   Don't understand how little damage a snapshot flash can do.
4.   Feel photos taking is not in keeping with the decorum of their
museum.
5.   Have an incredibly precious and delicate object, in which case it
probably should not be on permanent display anyway.
6.   Abhor ancient exploding flash bulbs, as described by Patrick
Boylan.

It's good if people take photos.  Photos enhance interest and help our
visitors bring the museum experience home.  Our visitors want to take
photos and why not!  Plus all those amateur photos aid your marketing
efforts.

Regards,

Joe Ansel