I am currently a phlebotomist at MMC. I have worked in this field (on and off) for the past 23 years. MMC does have a training programme for Phlebs,...but it is for people hired by NorDx (the hospital's lab). You best bet is to go through SMCC.
However, going through a formal phlebotomy class is not necessary to work as a phleb.
I know this is an old thread but if anyone is still interested I would try to look at adult learning centers or community colleges that are in your area. Some hospitals will offer on the job training for phlebotomy but you usually have to be an employee of the hospital first before you can get that kind of training. Those would be the first places that I would look. If all else fails you could call a local hospital and ask someone in the lab where they would recommend looking for training, they may know of some training programs that you don't know about or be able to get you in contact with someone who does. Good luck!!