I didn't have enough time yesterday to type up a proper answer, but I wanted you to have at least some information. For completeness, first my initial response.
Either the breaker has failed or there's a bad connection somewhere along the line. Check for voltage at the breaker and in each box along the line, the last box with voltage has a bad connection, probably one those push in connectors.
Based on your response, it sounds like the problem could be in one of the porch light connections where the power should continue on to the kitchen lighting. Which leads into your point to point question.
The wiring does loop back to the breaker, but not in the way you think, unless you have war time British ring wiring. Other than ring wiring, all conventional wiring is either linear or tree organized with pairs of wires (plus ground hopefully) making each run between boxes. Current runs up one wire, usually black in the US and brown elsewhere, and back along the neutral, usually white in US and blue elsewhere. In other words, the out and back is achieved in the same cable with a wire pair, not by separate cables. Assuming conventional non-metallic (romex) cabling.
Actually, alternating current doesn't go anywhere, it vibrates back and forth, but the direct current model serves conceptually to ensure power and neutral connections are properly maintained. Since circuit layouts can be almost anything, without a wiring diagram, only methodical checking of various wires in each box will reveal the actual layout. It's usually a safe assumption that the layout is roughly efficient in wire use, you're unlikely to see runs double back on itself without good reason.
Since the porch lights work on the same breaker and are fine, yes the breaker itself can be eliminated as a problem. It is possible the power connection that has failed is located in the breaker panel though, as two separate lines out of the same breaker could be possible, though somewhat unusual.
With that background, you should try to locate where the power runs from the porch lights to the kitchen lights. It may be from the switch or the light, or it may be a branch farther back towards the breaker. There may also be another box for something else between the porch and kitchen lights. You will need to guess at the probable layout to have any hope of locating the bad connection without testing the entire circuit. Wires typically run from closest box to closest box. Don't forget switches in two different rooms can be only inches apart for wiring, the boxes only happen to open into different rooms.
Also verify the power comes from elsewhere to the switch and not to the light. If there are only two wires, one cable at the switch, the power is coming through the light first, where you will find at least two cables and four wires. Unfortunately, there are also layouts involving three wire (plus ground) cables where where the power comes from is ambiguous.
A lot of talk for all you really are trying to do is find the other end of the wire which should have voltage but doesn't. Unfortunately, finding it is either a lucky guess or being thorough and methodical. I wish I could help more, but I can't be there to help you, but I am here fairly regularly if not frequently if you have any more questions. Good luck.
Best Answer