A question (And yes I have seen this problem before) Is the kitchen faucet the kind where you pull the head out and use it as a sprayer or is it the kind with the sprayer off to the side (usually right side?)
First kind: Where the hose joins the head, READ CAUTIONS IF YOU PROCEED
Pull the head out and unscrew the collar at the base of the head, CAUTION: if the collar falls back into the swivel part, it is dang hard to pull back out so put a towel over the hose below the collar or put a cloths pin on the hose.
Pull the hose out then you may be able to tap out a cartridge that is just inside the head, or you may be able to reach in with tools and pull it.
This is a multi purpose device, strainer, vacuum breaker, check valve.
Clean it well and re-install
See if it works now (NOTE you will likely get good flow from the hose with the head off.
For the sprayer off to the side types.
Remove the Aerator and clean it (The thing the water actually comes out of). same procedure.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times