You need to be careful as (being porous) you could damage the bricks.
My recommendation would be to start with the most gentle cleaners and then if you're not having success you could move to something more heavy duty. And remember to try it out on an inconspicuous area first.
You could start by just using a paste of washing detergent with some salt and apply using a scrubbing brush. If you don't have success, you could then move up to something stronger like Borax and then Shellite. - Jason
Try to avoid wetting the surface even though you might be tempted to clean with a soapy water mixture. Soot can be pretty oily, and adding water will only spread it around, creating quite the mess. Using rubbing alcohol and a dry cloth will be much more effective.
Eraser pads are also excellent for removing soot marks from timber and painted finishes. They contain a mild abrasive that helps remove surface contaminants. They also work on glass fireplace surrounds and become even more effective when used in combination with distilled white vinegar. - MitchellMc