Why is there no hot water in the kitchen after flushing our water heater?
First thing to check is the faucet aerator.  You're probably right about kicking sediment up and clogging something, if you're lucky its just the aerator.  It'd take a big piece or a lot of sediment to completely clog a 1/2"-3/4" pipe.

If it's not the aerator, and it's just a single faucet, you have to work backwards starting with the supply lines connecting the faucet to the shut-off valve, all the way back to the water heater.