The police suspected that Brian had broken the window at his house because he wanted to make them think that a burglar had stolen his valuable stamp collection. They thought that Brian had done this because he needed the money. However, they didn't know that Brian had flown to Brazil the week before, and was abroad when the burglary took place.
Why "had flown"? Is it because it is here to emphasize the innocence of Brian because it is obvious as it is written a week before that the fly happened before the police did not know, or is it to respect the backshifting done with "suspected" and "thought", or both of them — backshifting and emphasize?