I am writing a book report. The "that" in my sentence is referring to the book.
My sentence is
"In fact, many believe that it is deeply flawed."
Is this correct or should it be
"In fact, many believe it is deeply flawed."
Are they both correct and I should just pick one, or is there a better choice between them.
In fact, many believe (that) it is deeply flawed.
I think you mean that "it" (not "that") refers to "the book". In your example "That" is a clause subordinator introducing the underlined declarative content clause.
In the case of declarative content clauses, the subordinator "that" is sometimes obligatory, sometimes optional, and sometimes inadmissible:
(1) That I need help is clear. (obligatory)
(2) *I left before that he accepted. (inadmissible)
(3) I know (that) it's genuine. (optional)
The main place where "that" is obligatory is where the content clause is subject of the matrix clause, as in (1). It is likewise obligatory if the content clause is preposed so as to precede the subject, as in That I need help I can't deny.
"That" is inadmissible in a clause that is complement to a preposition like "before" in (2).
Elsewhere, "that" is in general optional, as in (3), and your example, though it is more likely to be omitted in informal than in formal style. Also, it is more likely to be omitted after short and common verbs than after longer and less frequent ones. For example, in This will demonstrate that it is genuine, the subordinator would probably not be omitted.