It's sometimes used in the Thelema religion he created. I remember reading in one of his books where he was talking about the black star and The Commodores' Signal Book and Vade Mecum. The book is literally just compilation/guide book/almanac from 1874 containing various signals, flags, symbols...etc for mariners and sailors while they are out on the heavy seas. Crowley read it and the liked idea behind these two flags of some oceanliner.
My best guess on the meaning of the anarchist black star version probably means the samething as the black flag does. I think it's more about the color than the shapes containing the color. Like the black star means African soliderity to African folk and people of African descent. The black in the pan African flag means the samething. Then there's Islam the OG of the black flag Islam. Can't top the original gangsta. The Hadith explains that it means legit struggle, victory, and fact bearers of Islam. Then there is the prophecy aspect of it. The prophecy is that an army will emerge from Khruasan (modern day Afghanistan) flying the black flag. From the emegerence of that army, Mahdi the Messiah will rise and Prophet Jesus will return both bearing the black flag alongside the army. They will bring forth a utopia and at the end the Prophet Jesus must die so the idea of the Trinity will be smashed. Mahdi the Messiah ultimate goal is to end the Trinity once and for all. That could be the plot behind a pretty good buddy/cop ultimate betrayel action film. Anyways, the Hadith says Muslims are to support and/or join the army of the black flag. the color black inside a shape also meeans the samething. Soooo... anarchism wise, the black star means the same as the anarchist black star. You've probably seen Islamists with one. Sometimes they write on it too. It would not surprise me if anarchists just jacked dat shit from Islam.
Here's something neat, the first people that really used the black flag were the Abbasid revolutionaries and they carried out a revolution. So the black flag has been part of a successful revolution. That gots to count for something.
When I have less free time, I'll try to figure out which Crowley book it was and to solve my own mystery. Vexillology books maybe interest of symbols on stuff like banners or flags.