I found the TSA stuff took about 2 weeks. This was in 2005/2006. One has to go to fingerprinting centre and get fingerprinted; the prints get sent direct to the TSA.
The Visa issues take much longer but it is just possible that a Canadian citizen might not need the M1 Visa for flight training. For the Visa, you need to pick a Part 141 school which issues an I-20 etc etc etc and then you can apply for the visa etc etc. It's all been done to death here - some sticky threads up at the top.