What role does previous knowledge play in the development of the story?
Not sure I understand what you mean by previous knowledge, so I'll assume you mean on the part of the reader. Since The Killer Angels is a novel about the Battle of Gettysburg, covering the events leading up to and including July 1 - 3, 1863 and the immediate aftermath, if the reader knows the basics about that event it helps in the understanding of the novel. Shaara doesn't spend a great deal of time in explaining who exactly the characters were and what their historical role was, and there are many different characters to deal with. So knowing who exactly the author is referring to when he says Lee, or Meade, or Buford, or Pickett, etc. makes a difference.
If I am reading about Day 2 and Little Round Top, it makes a difference to know about Joshua Lawrence Chamberlain and the importance of the position he was trying to hold, or the importance of holding the high ground, what a frontal or flanking maneuver is, etc. We also hear the use of military terminology specific to the Civil War, such as how units were identified, e.g. "101st New York, 20th Maine" and it helps to know how the draft worked and how military units were organized in those days.
I'm not sure if I understand your question, but I believe the previous post (by brettd) gave you some excellent answers. It would certainly be beneficial if the reader had a general historical background of the Battle of Gettysburg and its participants. No doubt author Michael Shaara researched his subject well: Since the unique quality of the novel depended upon the fictionalized dialogue between its characters (there is very little--if any--documentation of any specific verbal messages or thoughts of the commanders), the author must have thoroughly done his homework. He does a fantastic of job of getting into the heads of the characters and revealing what they may have been thinking. Shaara was inspired to write The Killer Angels after a visit to the battlefield with his family.