Please keep it spoiler free, I have finished The Black Prism and The Blinding Knife and just started The Broken Eye. I don't really know who the black prism is or what it is and how it's relevant yet. I mean it is established that Gavin is the prism early in book 1 but no reference is made that I can recall of a "black prism".
Although we are given hints throughout the series, we are told outright at the end of Chapter 19 of The Blood Mirror.
With Dazen trapped in his own prison, he is confronted with is most cruel creation: a piece of himself designed to distract his brother. This piece of himself still has all of Dazen's memories up to the split, almost all of which Dazen erased himself by using Black luxin.
During this particular revelation, we learn much about the backstory of the Guile brothers. And then, we are given the answer explicitly:
This version of Dazen reveals that Dazen is the Black Prism: "They knew you had to be stopped. You, Dazen, are the Black Prism."