Some of the decision depends upon the K program, I think.
Our K program was half-day non-academic, and we had a wonderful teacher who "got" our child and did a good job of differentiating what academic work there was for him. He mostly played at school and learned at home, and that was fine. It wasn't until he hit 1st grade--full-day, highly academic--and things went wrong fast!
In our situation, 1st grade would have been the year to skip, not K. (We chose to homeschool instead, but I think skipping would have been a workable choice, too.) But I really think it depends on what K and 1st are like at your school.
FWIW, I think Deborah Ruf's book also suggests that skipping 1st can tend to be better than skipping K, assuming K is more play-based than 1st grade is and the child will be able to learn at home. If K is academic, though, then I'd say skipping makes sense.
