Cut the old flooring out or cover with new plywood and stain.
Em's solution is the easiest. Also remove the toe kick trim, which is at the bottom of the cabinet. Make sure there is no other hidden water damage or that mold has not started to appear. Completely dry out the area before closing it in again in order to prevent any future mold growth.
I agree with both Erin and Seth, that is the best way to go. I hope this helps you Kay.