trisodiumphosphate TSP .... this is a water soluble crystalline material... cuts grease.... cleans soot....

I like what Barbara Todaro says. Sounds official 

Depends on what you're trying to clean off of the bricks. If smoke and soot, Akemi Stone cleaner. I've used lots of cleaning products for brick, concrete, stone, and monuments. Elephant Snot, Shadow Max, Brio Action 3 by Tenax, Borax, Akemi, D2, Heritage Restorer, NMD80, etc. Sometimes just white vinegar and water will work. Stone Cleaner Spray by Akemi- "Slightly alkaline cleaning agent. It is free of phosphates and lyes and biologically degradable.
 Used for thoroughly removing building dirt. Removes coats of stone polish and wax, slight concrete films, oil and grease, soot and tar, the remains of synthetic paints as well as plaster on all natural and artificial stone such as marble, travertine, terrazzo, granite, brick and cotto slabs, tiles, fair faced concrete and fine stoneware."

Looks like Barbara Todaro has got this one covered, or shall I say cleaned, for you! 

Sledge Hammer

I know this sounds wierd but there will be lots on answers on Pinterest. All I know of is muratic acid which is serious stuff.

Barbara's suggestion is probably preferable to a sand blaster.

Perhaps painting is a better option.

No clue, Will. When I had brick homes, I'd have them pressure washed...but that's hard to do inside. Probably if you google it, there will be some suggestions.

I am not about to argue with a former chemistry teacher, Barbara Todaro! 

Looks like you need to invite Barbara Todaro over for a brick cleaning hoedown!

I agree with Barbara Todaro on TSP.  It used to be in our dishwasher detergent too, until the people's republic of Kalifornia banned it.  That's why dish detergents didn't work worth a darn for many months.

This is what we use, haven't found anything that works better.

Barbara Todaro has a great suggestion for you. 

No F/P here but in PA we had a huge walk-in. Barbara Todaro has the answer while we simply gave up on cleaning ours. It builds some personality along the way. That being said the chimney flue had its annual washdown. 

I have no idea perhaps google it....

Will,

Barbara Todaro has your answer.  A

Carefully.

Barbara has the same idea I have

A good stiff brush, soap & water, and have a wet vac handy Will Hamm .

Red brick cleaner?

Hot water, Baking soda and elbow grease.

Jeff and Barbara have given suggestions that should keep you busy for month.

Unfortunately, you would be wise to start in an inconspicuous place. On a fireplace, I don't know where that is.

Let us know what worked for you and if any fatalities resulted from the process.

Paint?

I don't have a clue, Will! Hopefully someone has a great answer for you!

You have some good suggestions.

No idea. It's pretty porous, so tough to clean.