You are using a combo brush. For black algae, you need a stainless steel algae brush.
Nylon is for vinyl, fiberglass, tile, and plaster that is less than one year. (Plaster includes any exposed aggregate and marcite finish, btw!) Combo brushes are for older plaster. All stainless are for algae (very stubborn green algae and also the ONLY brush for black algae.)
You CAN unscrew the Wall Whale from the nylon brush it comes with and screw it on a combo brush if your plaster is over a year old. Newer plaster is really too soft for anything other than a nylon brush.
Any pool store, correct?
I'm not up to speed on your CYA level but if your target for the day is 6ppm, then run an 8ppm til the algae is gone. Brushing the black algae will not get rid of it in one day. Neither will chlorine alone. The stainless steal brush you are going to use is going to scratch the biofilms off the black algae. Think of it as exfoliating your skin. You open your pores and add cleaner and such right? You are opening his pores so the chlorine can penetrate it and eventually kill it. It takes time as black algae is a whole nother beast than green/poofy algae.
So brush daily and run a slightly higher FC level til it's gone.
I don't think that brush would work. The pool brushes have separated wires that fan out for more scrubbing power .
You can order one online via Amazon... specifically designed for pool like these:
10" easier on my middle aged arms:
http://www.amazon.com/Poolmaster-20..._sim_lg_8?ie=UTF8&refRID=1HGJSY7FBRXJJ5KD3QYJ
Or you can get a 21" like this one:
http://www.amazon.com/Poolmaster-20..._sim_lg_3?ie=UTF8&refRID=0ZQ6MFMNHP8ASSDW6B7K