How long to pump well out for
In general, moderate silt won't damage a typical electric well pump, as there are no close clearances (virtually all are not a piston with seals, it's a set of impellers which have space between them and the silt just flows through with the water.) 

Heavy sand over long periods of time can cause significant wear, but that does not look like what you show, and in any case you either have to live with it, (and replace your pump more often) or possibly reposition the pump to try and minimize it. You can use various filters to keep it out of the plumbing if it persists, but it may not persist once you have flushed things out a bit.

Are you pumping into a 5 gallon bucket inside the building? Put a hose on, run it outside, and run it for an hour or so, keeping an eye/ear on it so you can shut it off just as soon as water stops coming out, if it does. 

Pay attention to when that happens, and make the occasional check of how long it takes to fill a bucket for an estimate of flow rate (which will vary over time as the water level in the well drops) and you can get an estimate of your well's recharge rate. You'll also get an idea of how the silt is progressing. If your well recharge rate is high enough, it may just keep pumping the whole hour, that's fine. 

Leave it several hours or a day to fully recharge, and repeat for perhaps a week, perhaps less depending what you see for collected silt.

Your previous post has some data regarding the "volume of water in the well" which implies a 6 inch casing and counting the water below the pump (10 feet off the bottom of the well) which you cannot pump. In reality (if those figures are still accurate - water-tables not being fixed) you have about 110 gallons "stored in the well" you can access, and anything more than that you get out over a period of time informs the recharge rate of the well (typically stated in gallons per minute.) So if you pumped out ~200 gallons over the course of 30 minutes and then the water stopped, you could infer that about 90 gallons flowed in over the 30 minutes, implying 3 gallons per minute inflow. But if your pump pumps out slower than water comes in, the water would never stop - but you'd still have a number for the minimum rate of inflow you could infer. That's merely information, but it's often good information to have. 

In "flushing out the well" you certainly want to pump out MORE than the "stored volume" each time, since water WILL come into the well (and if the well has not been used for a long time, the initial inflow may indeed carry some silt with it.)