Kitchen faucet comes on strong but then tapers off

[Cadaverous Pallor]

Disclaimer - I don't know anything about plumbing.

Definitely a pressure problem. Pressure builds up when it's off which is why you get a decent burst to start (and can mitigate it if you don't turn it all the way on). However, I don't see how the faucet itself can be to blame. Is the kitchen on the far side of the house, away from your other faucets? There must be some issue with water getting to this particular spot.