Recently when we had heavy rain it leaked around the baement fireplace. I have noticed that the grout around the bricks are wet (not sure if soaking up from the floor). Thought because some flooding near by that it was a one time thing. Now it rained a coupe of days ago and I am noticing that it is wet again around the fireplace in the basement only. The fire place for the living room & the basement are connected. What could this be from.

The two fireplaces don't share the same smoke shaft in the chimney. You could possible be getting rain down the chimney but not likely. It is mostlikely that the footings of your basement fireplace are settling away from the foundation and allowing seepage.