For a study I need to know what are the most frequent flights in the World.
As a sample, how many flights from New York to Miami happen per day,
week or month? What destinations between aeroports (direct flights
only) are the most used? The answer should be in order of number of
flights, i.e. 1st miami-london (xx flights per day) 2nd.... etc.

Perhaps, you need to reword. In a sence nearly all flights are direct
flights, with the aircraft going somewhere else next. New York is
likely one end of the most non stop passegers between airports, but
New York City has two major airports. Treating the two New York City
airports separately; Chicago likely has more non-stop passengers.
Atlanta, Georgia is another major hub. Sorry I can't make a good
guess, if you want only one pair of airports.  Neil