How to clean textured brick fireplace?
I have white terrazzo floor.  It is very hard to clean.  I tried straight bleach on it on a corner, and believe it or not it helped alot.  I never tried on brick, but maybe you can try in a hidden spot, and see how it works.  I just put the bleach on straight, and aired out the room.  I did it like 3 separate times.  Got great results though.  

On my walls in my house, I use degreaser in a spray pump bottle.  If the area was dirty I sprayed with degreaser, and it seemed to clean all areas of my house pretty well.  Again, never tried on brick, but could try on a hidden spot, and see if it helps.