I imagine a situation must happen sometimes where a telescope watching a very dark object may catch a bright flash of light or a reflection off of a satellite. If that's even a concern at all (maybe all such telescopes are already designed to exclude that possibility), what countermeasures against blinding someone's eyes or frying the digital photo sensors are there?
Random bright objects can occasionally appear in astronomical images. Examples include asteroids and satellites. However, these objects are not moving at the sidereal rate across the sky, and thus unless the telescope is set to track them, they leave a trail across the image.
This is unlikely to cause damage and CCD detectors are fairly robust to saturation of exposures in any case. However, it may ruin the image.
Unless you happen to watch a nuclear explosion or a gamma ray burst or anything like that (very, very unlikely), no ordinary object in the night sky reflects or emits enough light to damage your eyes or fry your chip. Partly because they are very far away.
The only thing in the sky that can and will do that is the sun. So if you are watching at night, you are perfectly safe. So is your camera.
What can happen is that watching the moon or Jupiter can wreck your eye's ability to view faint or dim objects. Eyes need up to 30 minutes (give or take) to adapt to solid darkness. Brighter objects will partly or completely reset that ability so you have to wait a while until your eyes are truly sensitive again.
Imagine this: The moon is the brightest thing in the night sky. You can watch it all night long. If you use a bigger telescope, a gray filter might be nice, but it's not bright enough to heat your eyeballs. Numbers on the internet range between 1/400000 and 1/1000000 as bright as the sun.
While I agree with all the other answers here that no satellite flare has any chance of being bright enough to damage eyes or instruments there are concerns about them wrecking observations. Wikipedia reports that Iridium flares can reach magnitude -8 or brighter (Venus can be -4, the full moon is -12) and that could certainly be bright enough that scattered light from it would drown out some dim star or galaxy that you were trying to observe. If the flare can be predicted then you can always shut off the detectors for a short period, but some flares come from out of control satellites that are tumbling unpredictably.