One of the most useful ways to utilize harmonics, besides color and pitch changes, is to facilitate fast passages in the third octave of the flute.
By using harmonics of the octave or fifth (actually twelfth, but for simplification purposes we’ll refer to them as fifth) we can avoid some of the awkward cross-fingerings inherent to the third octave.
Below let’s examine some passages of the solo and orchestral repertoire where harmonic fingerings come to our help.
Chaminade - Concertino
6th measure of the Presto, original passage (not the ossia)
Play G3, F#3, E3, D3 and C#3 as harmonics of the fifth (C, B, A, G & F#).
G3 
F#3 
E3 
D3 
C#3 
Alternatively, this passage could be played with harmonics of the octave (G1, F#1, E1 and D1).
Jolivet - Chant de Linos
3 measures before the end
This passage can be played in 2 different ways: 1. as harmonics of fifths with an alternative fingering for A3, 2. as harmonics of the octave
1.
D3
F3 
G3
A3 
2.
D3 
F3 
G3
A3
Borne - Carmen Variations
Play the thirty-second notes F3, E3, and D#3 as harmonics of fifths (Bb, A and G#).
F3
E3 
D#3
Or use the following fingerings
F3 
E3 
D#3
OR
D#3
Tchaikovsky - The Nutcracker
Play the run with harmonics of the octave, excluding the Bb3. The Bb3 can be played as a harmonic as well, but since it's pretty exposed I advise not to do so.
Bb2
C3
D3
Eb3
F3
G3
A3
Bb3 
Ravel - Mother Goose
Please note that the first line of the system is played the first flute and the second line by the piccolo.
Starting at 9 measures after #7 use harmonics of the fifths for G#3 and F#3 (C# and B).
G#3 
F#3
A#3 
To facilitate the passage in the second octave starting at #7, leave down the F# (the Right Hand 4th finger, or ring finger) for A#2, G#2 and C#2. That works for the piccolo part as well.
Prokofiev - Classical Symphony
In the passage 2 measures before L try the alternative fingering for A3, and harmonics of the fifth for F#3 and D3.
B3 
A3
F#3
D3 
To read a more extensive article that I wrote about Prokofiev's Classical Symphony click here.