So, it's a common element in fan-theories and fanfictions that Kaito and Shinichi are the same age. But, I don't think so.
Let's pretend for a while that time has some meaning in the DCMK universe, and that the protagonists aren't eternally in the second year of highschool.
Kuroba Kaito is at least a year older than Kudou Shinichi.
When Kaito's story starts out, he's in his 2nd-to-last year of highschool. In the MK manga, he takes a break from being KID for exams (and a cold), so Kaito is probably in or about to enter his final year of highschool at the end of the MK manga.
After the events into the manga, (an unknown amount of time) the clock tower heist happens. It happens before the events in Shinichi's manga. From how everyone is dressed, the it was in the summer.
At the beginning of Shinichi's story, Shinichi and Ran are wearing light coats, and winter school uniforms at school, and there's no snow, which means it's either spring or fall. Since it was a big championship that Shinichi was congratulating Ran for, it was probably toward the end of the school year, beginning of the next, which would make it spring. Since this outing was planned, they probably put it off 'til after exams were over. So, we meet them probably at the beginning of their 2nd year of highschool. Also, Shinichi is able to transfer into the 1st-grade class as a child with very little trouble, and they're only just starting to learn addition. That makes it the beginning of school year.
Therefore, Shinichi is at least one year behind Kaito in school, and at least 11 months younger than him. Though, because we don't know how much time is between the MK storyline and the DC storyline, Kaito could be out of highschool by the time that they faceoff at the clocktower, and he could be as much as 3 years older than Shinichi.