A brick chimney that is more than 30″ wide needs to have something called a cricket on the uphill side of the chimney. It is sometimes called a saddle. A cricket is a pyramidal feature that diverts rain water to either side of the chimney. Without it, the water running down the roof slope to the flat edge of the chimney can accumulate against that chimney edge, and the pressure can create water intrustion into the chimney. Additionally, chimneys should have step flashing on the sides and flashing on the downhill side of the chimney.
While I don’t recommend installing chimney flashing yourself unless you have experience with this kind of work, the following article from Family Handyman provides a great overview of how your chimney should be flashed, and what you should look for in a properly constructed cricket.