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.