tl;dr: no, Hitler didn't survive the war, yes, he did shoot himself.
Short Answer is No.
I haven't read that book and I don't intend to. Now as for the evidence of the death of Hitler. First thing is that we have the testimony of numerous people who were in the Bunker when Hitler killed himself. Now the other thing you always have to think of when it comes to conspiracy theories is this. Hitler was the most recognised person in the world at the time. In order to get past the Army that surrounded Berlin would be next to impossible. Second once we get past that he needs to be able to get out of Germany which other Nazi leaders tried most all of whom failed except for a few lower level Nazis like Eichmann and Mengels. Lastly you have to think of Hitlers psychology he would not even want to flee since he refused to leave when offered by many senior Nazis who wanted to flee back to the Hills of Bavaria and make a stand there.
Hitler Nemesis Sir Ian Kershew Hitlers Dark Charisma Laurence Rees