Some children of narcissists do turn out to be narcissists themselves. At present the jury is out on just how much of the narcissitic personality type is inherited , at least expressed under the right conditons, and how much is learned behavior. The remainder of the "normal" children of these parents end up with a host of life problems that therapy is useful in dealing with.
I think Karyl McBride, in her book: "Will I ever be good enough?" talked about the various survival strategies that are available to children being reared by at least one narcissistic parent. (Please excuse me if I am mis-attributing this work - I don't have the book in front of me ....) I believe she suggested that children can survive by rebellion (making me link Otto Kernberg's work on the similiarities between narcissistic and antisocial personality disorders); survive by compliance or survive by identification and replication. I think that it would be the last group - those who survive by identification and replication, that would most closely look like they "inherited" narcissism from their parent(s).
But it does raise interesting questions - how much of personality is inherited? (Nature vs. nurture). If someone has come to a narcisstic personality disorder because they imitated that with which they were raised, are they more or less amenable to change as an adult? Inherently, what are the differences between the kids who [chose] different survival strategies? And, what about the parenting styles of people who survived being raised by narcisstic parent(s) - how are they alike and how are they different?