Hi, Kim. Let's see. You want to take a brick fireplace that will hide dirt and soot marks pretty well and paint it white so it will show off the dirt really well. And you want to paint so you cannot be able to clean the dirt and soot anywhere nearly as well as you could clean the brick. Along the way, you want to take an architectural feature that adds thousands to the resale value of your house and make it unusable and worthless. Does that sum it up well?
But I agree with BEG, you can change the brick if you really don't like it. Most brick fireplaces are a brick vaneer. The brick that you see inside the house does not match the brick that you see on the outside of the chimney. So you can have the inside brick removed and replaced with stone or other brick. There is a tremendous variety of stone, marble, tile and other products that you can use to replace the brick that you don't like. Granted, it will be more expensive in the short term than a paint job but the paint job will be more expensive in the long term when you go to sell your house. A nice fire in the fireplace was one of the things that really sold me on our current house but I would not even consider buying a house with a painted brick fireplace.
I suggest that you start with checking top of the line tile stores for marble or other stone that could be applied and go from there to masonry supply stores that have other types of stone products and can put you in contact with masons that can help you make the change.