I have hot water in all the faucets, but just a trickle in the kitchen. What could be problem?

Since it it only hot side you can rule out any area of the faucet carrying tempered water(aerator, sprayer, etc). If you have multi turn stop valves under the sink it is most likely the rubber inside has broken apart and clogged the supply line or cartridge. Start taking it apart and see where you lose pressure when you turn the shut off on. Beware, if the rubber is the problem the valve most likely will not turn off all the way.

Hmmm...

If this is strictly an issue with the hot water at this faucet then I would shut off the hot and cold water shutoff valves to the sink and then I would remove the faucet cartridge/washers and clear/purge the faucet/supply lines of sediment/debris (i.e., turn shutoff valves on while keeping a towel over the faucet). Inspect the parts and if necessary replace cartridge/washers.

If you have trouble shutting off the shutoff valves as Macplumb suggested (welcome Macplumb) then the shutoff valves may need to be repaired/replaced on top of clearing the valve of "stuff"!!

Back to you...

Mark