You can always safely assume that I am talking about playing music on your stereo in your living room. Normal listening volume for a flute would be well under 45dB. Subtract 30dB from that and you're down in the typical noise floor of a suburban living room. Assuming other instruments are playing along with the flute, and masking by lower octaves, you would never be able to hear an upper harmonic down that far.
In practice, the first three levels of harmonics, or about two octaves, are the most important. Beyond that, unless you're talking about cymbals or triangles or bells, the sound is generally at a very low volume level and can't really be heard in music at normal listening levels. Some engineers figure three octaves rather than two. That's fine too. This stuff is important when you're doing a multimiked, multichannel mix and you're EQing each instrument separately.