Is the kitchen faucet the only problem? If not, then the water heater or other problem may exist in the water system.
When you run the hot water, are the particles always coming out or do they go away after while?
Black particles can be caused by carbon water filters. Do you have a filter? Those particles stop over time.
Washers and "O" rings that are wearing out can cause black particles. I would check under the sink to see if you have any slow drips. You may see white, green or black colors along the fittings.
I've also seen black particles from algae in the line. Maybe there's a leak somewhere in the system that dripping and cause the algae to form? Inspect your water lines and checking for leaks anywhere in the system may help. If you turn off all your faucets, washer, hose bibs and check the water meter, is it still moving? I'd check it every 15 minutes for an hour to see if there is a slow leak.
Here's a diagram that shows all the parts: PlumbingWarehouse com Delta Kitchen Faucet Parts For Model 470 472
I'd also take out the aerator and see if it's clogged.
You may have to change the washers and "O" rings.
Parts and prices: (sample list)