Why do my pipes bang when running hot water in my kitchen?
You have a valve failing somewhere in your plumbing system, the trick is to figure out which one. If this only happens with your sink, then I would start there.

If your sink has a separate sprayer on a hose, then it's possible the diverter valve is flapping, trying to send water to the sprayer. If that's the case, it could be as easy as a blockage in the aerator of your faucet, which is often easy to remove and clean.

If that doesn't solve your issue and it's isolated to the sink, then I would try replacing the valve/cartridge in your sink fixture, or you could replace the entire fixture.

Beyond that, you'll need to work on a process of elimination to figure out which valve is causing the problem. There are likely shutoff valves under the sink, another at the hot water tank, and another for the house.

One last device that I've seen cause pipes to bang is a failing pressure reducing valve (PRV) that is bell shaped and found just after the main shutoff in some homes. This seems less likely in your scenario, since the last time I heard one cause pipes to bang was after I turned off the water and the pipes would rattle as the PRV allowed pressure to rise past the designed threshold.