Flute harmonics enter one by one about 80 ms after the fundamental begins.

Evidence

The higher harmonics enter one by one approximately 80 ms after the fundamental starts. The rather long note onset phase is characteristic of a flute note played with some deliberation. The periodicity in the waveforms develops gradually, and in all cases there is an appreciable time over which the amplitude of the waveform reaches its steady state. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1452

Related

• Flute notes have a characteristic breathy onset with harmonics entering gradually after the fundamental (similarity 0.87)
• Instrumental notes begin with the fundamental before higher harmonics appear (similarity 0.87)
• Musical instrument notes have a gradual onset before steady state (similarity 0.82)
• Flute and piccolo span B3-D7 and B4-D8 respectively (similarity 0.80)
• Flute playing frequencies are impedance minima; trumpet’s are maxima (similarity 0.79)
• Note onsets are composed of many separable acoustic cues (similarity 0.79)