I use a rubber gizmo that connects to a garden hose and swells up to fit the drain pipe and the pulses and shoots a stream of water to push the clog along. Any hardware/home depot etc should have them.

Works great when a plunger isn't enough. You put it in the pipe until it meets the clog, turn on the water and it pulses for a few minutes (you can feel it vibrate the floor). Then turn off the water and see if will go farther in, repeat. I've gone 50ft (my longest two hoses) and it did the trick.

Most kitchens have a clean-out outside that you can open to get better access to the drainpipe.