A flight of stairs is a set or series of steps between one floor or landing of a building and the next floor or landing. (floor usually means a landing).
So, if the building had 5 floors, there would be 4 flights of stairs, one flight of stairs between the 1st and 2nd floor, the 2nd and 3rd floor, the 3 and 4th floor, and the 4th and 5th floor.
The American and Canadian Building Codes do not specify the number of steps in a flight of steps, however, the codes do specify the height of the steps, e.g., 7.5 inches (19 centimeters).