I have a very annoying squeal in my kitchen faucet.
When I take out the aerator it lessens but also causes a hammering noise.
I have not replaced or changed anything.
And this does not happen in either bathroom ,tub, shower or sink.

Close the hot and cold angle valves under the sink 1/4 of a turn and see if it will help, good luck.

John

I am guessing that your faucet has a spray hose attached, if so I think the noise is from your spray hose valve trying to close and open as you use the water. To replace this part you will have to disassemble the faucet and of course you will have to find a part for the brand of faucet that you have.