How do I fix the low water flow of my kitchen sink?
First confirm that the problem is at the valves and not a clogged faucet screen.



Backing-up the valve with an  adjustable wrench you could turn your knobs with channel locks but be prepared for a few drips, or something completely catastrophic to happen. Not something to be messing with on a Saturday evening. Being frank, those valves are crap. Preferably use 1/4 turn valves. Seeing that these are compression fitting, they're easily changed. Ask for these.



The choke point is at the valve, this clears the blockage: Once you have the valves spinning freely, shut them off and disconnect the leads at the faucet (back this up carefully, do not twist the copper leads). Run the lines into a bucket, completely opening and closing the valves several times. Reattach them, turn them on. Do not touch them again without repeating these steps. Remove the faucet screen and run some water for a bit. Reinsert a cleaned screen, done.