The Flight usually denotes a period of time during the early development of Psychohistory during which Hari Seldon was on the run from the Imperial authorities, mainly Emperor Cleon I and First Minister Eto Demerzel, in order to prevent them from using him and his fledgling theories to their advantage. Seldon was aided in the Flight, and in fact, was launched upon it, by Chetter Hummin, who introduced Hari to Dors Venabili and charged her with keeping him safe.
Of course, Seldon finds out in the end that Chetter Hummin is none other than Eto Demerzel, who is none other than R. Daneel Olivaw, the ancient robot. Olivaw had sent Seldon on the Flight in order for him to lay the foundation of Psychohistory, which Seldon soon found out could be done by observing the different sectors of Trantor and their interactions.
The Flight is completely narrated in the first Foundaiton novel (chronologically), Prelude to Foundation.