Which is the correct spelling flight or flite?

Both are words -- see below:

"flite
1. to scold or rail at
2. a dispute or scolding"

"flight
1. a. The motion of an object in or through a medium, especially through the earth's atmosphere or through space.
b. An instance of such motion.
c. The distance covered in such motion.
2. a. The act or process of flying through the air by means of wings.
b. The ability to fly.
3. A swift passage or movement.
4. A scheduled airline run or trip.
5. A group, especially of birds or aircraft, flying together."
http://www.thefreedictionary.com/flight

"Flight" is also used to describe a series of wines tasted at the same time.

https://en.wikipedia.org/wiki/Wine_tasting

A group of consecutive steps/treads as in "a flight of stairs"

The wings of a dart are also known as 'flights'.