No hot water from kitchen faucet yet there is still water flow through hot water valve
It sounds like a chunk of the washer in that valve may have plugged the line. 

I have seen similar issues with faucets where they won’t turn off all the way, this is usually caused from the rubber seal starting to fail. When you open the valve back up a chunk gets lodged and stops the water flow. 

The problem may be in the valve or it could have passed into your new faucet. 
The first step is to fix that valve , turn the water off for the house, remove the valve stem and inspect the washer if any of it is still intact , clear all the debris out install a new washer, plumbing stores have kits with a dozen or more in several sizes for just a few $ a good kit for any home owner to have. Reassemble the valve and close it keep the new faucet turned off.  Disconnect the pipe or tube from the repaired valve,

Next I back flow cold water through the valve to push any small chunks out of the new faucet.
With a bucket placed to catch the water turn on the new faucet to hot then slowly move to cold or open the cold valve, the water should flow backwards out of the pipe on the hot water side. Cycle from all hot to cold several times, if water is coming out of the pipe you won’t have to disassemble the faucet. Verify that when the hot is turned on at the repaired valve it flows. Reconnect the pipe to the repaired valve. And everything should work.