Question

in flute which vibrating part produces sound

Answer 1

In a flute the sound is produced by the vibration of air present in the flute.
You can say air column produces sound in a flute.

Answer 2

The vibration of column of air inside the woodwind instruments result in production of sound. Flute is also a type of woodwind instrument. Air is blown across the top of the instrument then a stream of air is passed through column which splits making sound. Half the stream moves past and half of the air stream vibrates inside producing the sound effect in flute. The vibrating section is called the standing part of air in the flute column.