There's also Pinoko to take into consideration and how long he's had her that you have to add on. He got her after he lost his medical license.
22 is waaaaay too young for Black Jack. More likely, as pointed out by Shiyonasan, Tailz and me he is in his 30s. Though he LOOKS like he could be younger.
As for Kei well he probably isn't too much younger (or older) than Black Jack. I don't think it EVER made any sort of inclination to his age so that's up for interpretation

I really think personally that he's closer to 35 or so.
~~EDIT~~
So I got curious and decided to just do some research to find out how long it really takes for a Japanese citizen to become a Doctor/Surgeon in Japan. It's different from here in that they don't necessarily have to obtain a bachelor's degree in order to get into a proper medical school, as some (not all, most transfer from a university) can enroll in med school right after graduating high school. Medical school in Japan is 6 years of grueling exams and whip-cracking teachers, and then after that the student spends about 2 years of 'on-job' training. This could be said to be an internship, it is usually unpaid.
So for Black Jack, someone who is very bright he probably entered med school right after high school (age 18) and spent his 6 years plus two (that would make him 26 when he obtained his medical license) in medical school. From there one can speculate how long he had his medical license before he lost it, tack on the year he spent looking for his perfect location, the year(s) he spent actually practicing renegade and then Pinoko's time with him to get a good grasp of his age which would put him well in his 30s as we've agreed on!

Also I'm a little lost on some things that I've found out... I'm also speculating on how long it might take for one to become a surgeon in Japan. The information I was able to find was only for becoming an MD essentially, not a specialty field which is a surgeon. From what I have been able to find they do have to have a few extra things in order to become a specialist which is yet ANOTHER 4 years or so after they get their MD. Though I'm not sure as what I have been finding has not been entirely clear or readily available to those outside of Japan.
Most of what I have been finding is information for foreigners on how to practice medicine in Japan, not internalized information for the Japanese.
This article has been the most helpful in what I have found; http://www.eltnews.com/columns/uni_files/2010/02/qa_time_about_medical_students.html