When I turn on the kitchen hot water, it heats up, then rattles, and the pressure cuts back by at least 50%. This does not happen with the dishwasher or the cold water. Any suggestions?
If you're only opening it just a bit, then it can be thermal expansion. When the hot water reaches the valve, it can cause some component to lengthen slightly, closing the valve a bit more than it was.
I've seen that exact behavior on bathtub valves as well. If the behavior is new, it could be that a washer is staying compressed when cold and is expanding only when it gets warm. If so, replacing the washer may change it up.
Does it cut back 50% if you open the valve all the way, or only if you open it a "normal" amount?
The faucet needs rebuilding with a re-build kit specifically for the faucet, some faucet's rubber seats collapse as they fail & dramatically reduce flow.
The other possibility is that a piece of large debris got caught within the faucet & only releases to block the flow with hot water. This may be successfully back-washed out, but usually the faucet has to be replaced.
If it's not an older house with screw-retained compression washers (the screw heads can rot out & fall into the house piping to end up in faucets), then debris of this size could indicate interior pipe corrosion or that piping valves & Shut-Offs are built-up with water deposits & both should be operated to scrape-off or break-off any build-up.
I would replace the hot shut-off valve below this faucet and the line from there to faucet. If this is the only faucet with this problem, then this is your logical first step.Many of these small shut-off valce are prone to becoming blocked.