The phrase "flew towards" is correct and can be used in written English.
Example sentence: The eagle dove swiftly and flew towards the mountains in the distance.
Some flew to slip, others flew towards fine leg.
Steps, escalator, sprint, Ant flew towards the Piccadilly line.
After an initial orientation phase, butterflies flew towards the maximal inclination available.
The wind was behind us and we flew towards Haarlem, freewheeling for long stretches.
Sangakkara cracked Pollock's delivery hard and the ball flew towards Amla.
Dhoni cut hard and the ball flew towards the third man boundary.
You lift the cup and it "flies" towards you, as you applied too much force.
The drones were flown towards Maduro as he addressed soldiers in Caracas on Saturday, officials said.
The plane was flying towards a large storm system, a common obstacle on that route.
One bird flies towards a branch; another's nearby chirping sounds begin.
People described how coalition helicopters were seen flying towards the crash site.
