When I turn the hot water on full I hear a loud rumbling sound coming from the faucet/plumbing. Any idea what it is or how I can fix it?

You may have some debris in the valve or cartridge. Shut off the water below the sink at the stop cock. Is this a single handle or double and does the rumble happen with both hot and cold?

What brand of kitchen sink faucet do you have? Does it have one handle or two?

It's a bathroom faucet with two handles. It only makes the noise when the hot water is turned on.

OK, you only need to shut off the hot supply. Remove the handle of the faucet and then the hex ring that holds the stem. Withdraw the stem and flush and inspect for debris. Also check the seat for debris and/or burrs. You should be good to go but write back if you hit a snag,