First a brief explanation of what flickering is:
Flickering is caused by transient changes in light intensity. It is much more common to see flickering in small / point sources of light (e.g. stars or planets) because very small atmospheric changes affect all light arriving from that source.
Similar small atmospheric disturbances usually don't affect all the light coming from non-point sources like the moon.
The most simple and plausible causes of "moon flicker" (changing brightness) would fall into one of these categories:
- Something interferes with the passage of light from Sun -> Moon
- Something interferes with the passage of light from Moon -> Earth
- Something changes the brightness of Moon
A. The Moon emits light
B. The Moon's reflectivity changes
C. Something else shines on the Moon
- Something changes the brightness of the Sun
1. Interference of Sunlight reaching the Moon
I really can't think of much that could do this. It'd have to be huge to affect the brightness of the Moon such that we could see it.
The Earth's atmosphere isn't in the way so that wouldn't do it either.
Under the realm of SF, you might see something like this if you had something like a planet size solar reflector (e.g. to cool Venus or warm Mars) and it accidentally reflected light onto the Moon. That might be spectacular but I'm not going to do the math for you :P
2. Interference of light reflected from Moon -> Earth
This is by far most plausible since the Earth's atmosphere regularly causes flickering in the light coming from smaller astronomical bodies. To affect the overall brightness of the Moon, the turbulence would have to be much larger than normal (more energy in the atmosphere).
Alternatively something large would have to pass between the Earth and Moon to dim the Moon significantly. The closer the object is to the observer, the smaller it could be to have the desired effect. That object would probably possess low reflectivity (perhaps an undiscovered Near Earth Asteroid?) or the observer might notice the occultation.
3. Something changes the brightness of the Moon
This image of Inconstant Moon from Deviant Art
There are three phenomenon that could do this, two from a flash coming from the Moon and the last is something else shining on the Moon.
Moon emits light
The more common of these and one that has been observed is meteors striking the Moon. If you are not observing the Moon with the telescope, you'd just see a brightness change without knowing what caused it. The meteor actually emits enough light to compete with the reflected sunlight. It especially striking when the Moon is not full and the meteor strikes the unlit portion of the Moon.
Here's a video of a meteor striking the Moon
Moon's reflectivity changes
Probably less common but possible in an SF story would be if human development left man-made structures on the Moon. When sunlight strikes flat surfaces (e.g. PV panels?), the terrestrial observer would see glinted sunlight. This might cause a "flickering" type of effect. The change in reflected could also be caused by any number of other SF occurrences.
Something else shines on the Moon
A variant of this would be if the Solar System were hit by a supernova/hypernova/gamma ray burst from relatively close range (10s - 100 light years). People on the sheltered side of the Earth might see spectacular effects on the Moon. In this scenario, the devastation would be total - it would kill everything on the planet.
4. Sun's brightness changes
A number of SF stories have been written about this. The most memorable to me was Larry Niven's Inconstant Moon (also made into an Outer Limits episode). In it the Sun emits and enormous flare that presumably kills most of the inhabitants of the days side of the planet. You wouldn't need such a huge flare to cause a noticeable difference in Moon brightness but I don't think the effects would be very benign either.