Leak from base of flue
To properly seal the fireplace flue, I’d 1) Install a flue cap, 2) put a cement “wash” between the flue and fireplace bricks for positive drainage, 3) Install a clear sealer on the fireplace bricks, 4) Install flashing between the fireplace bricks and the roofing material, 5) verify that the roofing around the fireplace isn’t leaking. 

If the flue only leaks during extra strong wind storms, I’d look at getting a flue cap that has a wind screen, like this:

http://www.google.com/aclk?sa=l&amp;ai=DChcSEwjq0drjitndAhWaj7MKHVATD84YABAfGgJxbg&amp;sig=AOD64_1Tlc34Pk7FQbwhjdDVtQj--CakTg&amp;ctype=5&amp;ved=0ahUKEwjy1NTjitndAhXLu1MKHVLuCtIQwg8ILQ&amp;adurl=