* 비행기편 = flight. The scheduled flight of an aircraft or the arrangements ones makes to take one.
* 항공편 = same as 비행기편, but a bit more formal. Sometimes it can mean the flight number.
* 비행기 편수 = 비행기편(flight) + 수(number) -> number of (scheduled, operated, available) flights.
* 편수 = abbreviation for 비행기편수, 항공편수.
편수 is not as common as the others. It is usually used when talking about how many flights are available to certain destinations (on a given day, week, month, etc).
"Flight number" is called 항공편명, 항공편, or just 편명(명 = name).