Sorry, but brick is not meant to be painted. Ever!
However, ther are ways to make the brick look good. Methods of cleaning it, etc.
A painted fireplace is only going to make your Formal Dining Area: look crappy, lower the resale of the house, create a maintenance nightmare, make a functional fireplace non-functional, etc. (the list could go on)
Please provide more information and others may have ideas for you. There are better solutions than painting!
If you simply don't want to look at it get an oriental decorative folded divider thing (I dodn't know the real name for them) to place in fromt of the fireplace.