What does Jane mean when she says,“He may live in my memory as the most amiable man...to hope or fear, and nothing to reproach him with," about Darcy?
This quote by Jane Bennett is found on chapter 24 (or vol.II ch. I) but, contrary to what your question asks, Jane was not speaking about Mr. Darcy. Instead, she was referring to Mr. Bingley, who is Mr. Darcy's friend.
Prior to this chapter, the Bingleys had abruptly left Hertfordshire and to settle in London for the winter season. This came as a surprise to the Bennets, particularly to Mrs. Bennett and her daughters, because, at that point, Jane had made a strong potentially marriageable acquaintance with Mr. Bingley, and had even become good friends with the man's sister. The fact that the Bingleys leave town without announcing it comes as a shock that results in deep disappointment for Jane, since she has had developed what she describes as an attachment toward Bingley.
Chapter 24 begins with the long-awaited letter from Miss Bingley explaining to Jane what had occurred, bringing Jane and Elizabeth to the conclusion that Darcy and his people have, in some way, coerced Bingley into returning to London and, similarly, into returning to their original interests in London. According to Miss Bingley, her brother has been basically "promised" to Miss Darcy (Darcy's younger sister), and so they decided to leave and return to their lifestyle in London indefinitely.
Understandably, Jane and Elizabeth feel pushed to the side and upset at the pretentious behavior of Ms. Bingley. Jane, who is not as passionate as Elizabeth, still manages to comfort herself within the painful times and says the words quoted in your question
He may live in my memory as the most amiable man of my acquaintance, but that is all. I have nothing either to hope or fear, and nothing to reproach him with
mainly promising to Elizabeth that she WILL forget Bingley, and that she refuses to keep her hopes up. That it will take time, and it will be painful, but that she refuses to allow these news to form her neither a bad opinion of Bingley, nor will it keep her dreams about Bingley alive. In fact, she even told Elizabeth the extent to which she is willing to forget about Bingley
You doubt me," cried Jane, slightly colouring; "indeed you have no reason. He may live in my memory as the most amiable man of my acquaintance, but that is all. I have nothing either to hope or fear, and nothing to reproach him with. Thank God! I have not that pain. A little time therefore.—I shall certainly try to get the better.
Therefore all this comes as a result of the sudden departure of the Bingleys, led by Darcy and Miss Bingley at that point, in order to remove Bingley from Jane and prevent that they would make their acquaintance into something more serious. This, we find out later, during Darcy's eventual proposal to Elizabeth; a proposal that goes awry quite fast.