Finding the phase of harmonics from a plot spectrum

I’m trying to recreate the sound of an audio file of a flute playing A4, 440 hertz by layering sine waves one by one playing at certain frequencies, amplitudes, and phasing for a project. I’m using Audacity’s plot spectrum analysis to find the harmonics and their amplitude, but I’m wondering if there’s a way to find their phase in order to accurately recreate the sound.

I know FL Studios Sytrus synthesizer has basically exactly what I’m looking for as it can analyze a single cycle waveform, but I don’t have access to this, however, if anyone knows of an alternative that can achieve basically the same effect that’d be well appreciated.

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