What is the actual effect flash lights from cameras have on materials?
That depends on the specific flash and the specific materials. From a physics standpoint, we can discuss the mechanism that can take place.
As light reaches a material, it has the potential to be absorbed. If the light has more than a specific amount of energy, it can transfer that energy to break a molecular bond. Breaking bonds degrades the original material. This photosensitive destruction can change the appearance (bleaching/fading) and compromise the strength of materials. Photodegradation.
While UV has more energy and is potentially more harmful, some materials are damaged even by exposure to visible light.
If there is such, how is it generated and how does it differ from other light sources?
Most camera flashes do not differ greatly from other lights. They may be more intense, but will not be on for long. Depending on the construction, they could generate higher frequency light than regular lighting, but almost any consumer flash is going to have UV filters to prevent significant amounts of UV from being released.
It's certainly possible to make flash bulbs that don't filter UV for special purposes as well, but that's not a standard flash. Those items would be more damaging, though.
Could an adequate-power-laser-show really harm a structure like an old pyramid? Are there any differences between the kind of erosion or decay caused by lasers and flashes?
In general, I would be completely unconcerned with anything outside. Unless it's some very special device, the flash or laser won't do anything that extended sun exposure hasn't done.
Limiting the total exposure of a painting is very different than worrying about the color of light you're shining on a stone outside.
Also:
Does flash photography really damage art? The persistence of a myth.