"fly nonstop" is correct and usable in written English.
You can use it to describe a journey that does not require any stops along the way. For example, "I'm taking a flight to Chicago that will fly nonstop."
Both Google and Facebook are developing low-flying, solar-powered drones able to fly nonstop to provide internet signal to places in the world where it is non-existent.
The two-way, weekend charter flights will also fly nonstop.
Some of these birds fly nonstop across the Gulf of Mexico.
THE BASICS Several airlines including Delta and US Airways fly nonstop to Asheville from New York.
IF YOU GO Delta, United, Continental and Scandinavian fly nonstop to Copenhagen from New York.
At least four other teams want to fly nonstop across the ocean.
Last month, Delta announced it would fly nonstop between Atlanta and Lagos, Nigeria, starting Dec. 3.
That permits it to fly nonstop between Vietnam and Europe or North America.
American, Delta and Continental also fly nonstop from the New York City area.
THE BASICS American, Continental and Delta fly nonstop from New York-area airports to Nashville.
