Air in the lines and pressure issue
IF you do have debris in the line, the best way to find it is to map your piping layout on a piece of paper and do some trial and error to see if any fixtures are not effected by the water pressure drop. Start at the furthest fixture and work your way to the meter testing one at a time, testing hot and cold separately. Does your hot water also loose pressure? if so, the clog might be before the take off to the water heater, if your hot water is fine, but your cold water drops, the debris would be after the water heater take off, if its both hot and cold, then it could be between the meter and the water heater and so on. If the front spiggot is right after the meter, test that line by itself, and if you don't see the same problems your getting at other faucets, then the issue is after the tee to the spiggot feed. test every single faucet and fixture by itself at full flow to see if you get the same problem like at the kitchen sink. If every single fixture is having problems, then your clog will be close to the meter. If you go through this exercise, you should be able to narrow down the problem to a small section of piping which would need further inspection or if you can isolate that section and blow compressed air backwards through that section to clear it out.
If you do this and still can't figure it out, the only recommendation I can make would be to shut down the water at the meter, drain the system, disconnect the line on the house side of the meter, shut off the valve to the water heater and any valves that tee off the main line to other fixtures that are working fine, then go to the furthest fixture and disconnect the cold water side, hook up a compressor to blow compressed air backwards through the piping system to see if anything comes out the open pipe at the other end by the meter. Let it run for a couple minutes while someone else is watching the open end on the other side. I'm assuming your piping system is copper for this to work. You don't nessessarily need high pressure air, you just need a compressor that can flow a good amount of CFM.