I mix equal parts vinegar and water to clean mine and remove soot. Spray on, allow to sit for a few minutes, then scrub off. If that doesn't work, you can purchase a product that is specifically made for fireplace brick cleaning. The vinegar solution usually works for me
Here is some info to help you.
Might have to use an acid cleaner as for patio concrete or bricks, as if you scrub to hard you will also remove and weaken the bricks. Soot seeps right into the brick core. Another way might be to use a flat paint to colour them back to required colour. Best wishes.
I've always used oven cleaner. I put it on cold and wait 5-10 minutes then rinse it off with a damp cloth. If the bricks are heavily textured then I gently scrub the bricks with a coarse brush, ALWAYS USING EYE PROTECTION AND RUBBER GLOVES. I have found this works on fireplace glass too, understanding you can't spray oven cleaner on Hot glass because it may break the glass. Always use the precautions on the oven cleaner can. Stubborn jobs may require repeating the job. It is surprising how easy it is too clean fireplace bricks.