Unfortunately, SimBiology does not give you the rates of your reactions at all. However, in order to run, SimBiology does calculate the rates. rateout.m records all rates while you're simulating.
This little tool needs to be incorporated as two simple rules in your model (the first as initialAssignment, the second as rate).
temp = rateout(-1)
temp = rateout(time)
This way the model saves the rates for all reactions in each simulation step in a global variable. Calling rateout.m from your workspace sorts through the intermediates and assigns all rates in your workspace (next to t and x, which SimBiology puts there anyway).
Detailed instructions are in the file itself.