Low water pressure in both kitchen lines -
Since the pressure drops for both hot and cold at this fixture, the problem is inside the fixture as you've already guessed. The first place to look is any aerator or filter screen on the fixture, debris gathering there will quickly slow the entire flow. Looking at the diagrams for your faucet, I believe that will be part P (the flow straightener) in this picture (Q appears to be a tool for opening the end of the spray assembly).



You can also verify the pressure from before the fixture is strong by disconnecting the hot and cold supply and running them into a bucket or drain to check the pressure coming from after the shutoff valves. 

The problem could also be in the mixing valve and you'd need to remove and inspect the cartridge if it's there. basically anywhere after the two water lines merge could have a blockage.