Our kitchen faucet was replaced about three years ago when we moved in. Every week or two, the flow starts to get noticeably throttled and I remove it for cleaning. What I find inside is a layer of small, dark brown flakes of a non-magnetic material. They seems like a hard wax or plastic. I have not noticed anything similar in the other aerated faucets. What is this, and should I be concerned?
That may be the rest of whatever, though I'm doubtful. But, the aerator will restrict flow, so run the faucet without the aerator at full force with the sink plugged for both hot & cold & see if anything noticeable flushes out. If it seems to clear out whatever then just put the aerator back on & see if it ever returns.
If nothing really produces from the unrestricted run, then it's probably a (or more) bad cone washer in your flexible supply lines under the sink. Those lines are only supposed to be very-very lightly wrenched on.
I suspect yours were way over tightened, which severely damaged the cone washers. They would be splayed out into the water stream & slightly eroded with every use of the faucet. If that's the case then it's nothing dangerous & just an avoidable nuisance.
Those black particles appear to be from an activated carbon filter that is probably failing. Check your house for one of the filter housings to see if one of these filters is present.
If it is activated charcoal particles, it says they are non-toxic and food safe according to the Brita website. Since you are only seeing it on the kitchen faucet, the filter may be located under the sink.
There is a similar question on Brita's FAQ page:
There are black particles in my water after filtering - what are these?
The black particles are parts of one of BRITA's filter media, the activated carbon. The granulated activated carbon is made of coconut shells. Like each natural product, coconut shells are subject to natural variances regarding product quality. This can lead to abrasion of parts of the carbon into your filtered water. To eradicate any carbon dust which may be present, preparation of your cartridge is crucial. Please prepare as per your cartridge instructions or see "How to prepare your cartridge". Please be assured that the contents of the cartridge are food grade and completely harmless to yourself and if accidentally consumed will be harmless to health. Their presence will not affect the performance of the cartridge. If there are still dust or particles present after this initial preparation, then we would suggest that the cartridge is removed from the system and re-prepared by: MAXTRA, Classic & Multifit cartridges: Vigorously shaking under water, then re-install and flush through with two litres of water. Inline, P 1000 & A 1000 cartridges: Flush a futher two litres of water through the cartridge.