Kingston (67) and Kaymer are at 7-under 203 heading into the final round at the Arlandastad course.
Paul Broadhurst, whose 64 was the lowest score of the day, and Nick Dougherty (69) are three strokes behind in third place. Broadhurst had seven birdies -- including four on the last five holes -- and one bogey.
Kaymer, a 22-year-old German who won twice on the Challenge Tour last year, is winless on the European Tour. He also shared the third-round lead at the Wales Open earlier this season before slipping to 14th.
Third-round co-leader Henrik Nystrom led after 12 holes, but the Swede bogeyed four of the last six holes and dropped to 10th.
Corey Pavin shot his third consecutive 70 to trail by seven strokes.