For sure you can capture a meteor shower with the 18-55mm kit. The question isn't so much about your gear, it's more about what kind of photo you want to take. With your gear, you can easily set your exposure time (shutter speed) to 30 seconds (or Bulb for indefinitely long). The longer it stays open, the more light will hit your sensor, and the brighter your image will be.
However, the longer you hold the shutter open, the the longer the meteor tails will be as the meteor light drags across your sensor while your shutter remains open.
So, if you want short tails or just points of light, you'll need to use a faster shutter speed, which means you'll need very clean high ISO or very large aperture (f/1.8 or f/1.2) to get an image that isn't very noisy.
However, comet/meteor tails are quite beautiful so I'd recommend setting your camera up on a tripod, opening the shutter up for 30 seconds at f/3.5 and 18mm using manual focus, ISO 6400, and starting there. Adjust according to taste.