This discussion of fingerings for six-hole flutes proceeds stepwise
through three levels of difficulty:
In the fingering patterns shown below, "x" signifies a covered hole and "o" signifies an un-covered hole. The embouchure hole into which you blow is understood to be on the left and is not shown.
In flutes of another key the same principle will apply - simply open the holes in progression to sound the main notes of the flute.
The difference between the first and second octaves, at least with respect to the main notes, is in how you blow the flute, not how you cover the holes. Practice with all holes open until you can blow two distinctly different notes an octave apart. Blowing the higher note will usually require that you blow harder. Rotating the embouchure hole toward you and away will help.
An alternative fingering for the lowest note in the second octave is
as follows:
D oxxxxx
One technique for sounding a note a half-tone lower than a given note, a C instead of a C# for instance, is to cover the hole only fractionally. If you slide your finger slowly over a hole you will discover that the tone of the note is lowered progressively. Considerable practice is required to get a reproducible result using this technique, but it is one approach. The technique is sometimes called "half-holing".
An alternative is to cover one or two or three or more holes below the highest open hole. This technique is sometimes called "forked fingering". Progressively lower tones are commonly qchieved as more holes are closed below an open hole. Experiment will tell you what pattern gives a good result for a particular flute - not all flutes behave the same when using this technique! Particularly, a large hole, perhaps 1/2" in diameter, will require more holes to be covered than a smaller hole if the objective is to lower the note a half tone.
On a D flute you can try the following experiment to discover how best to play a C in the first octave with forked fingering. First, blow a C# (all holes open)
C# oooooo
and then, closing holes progressively, try the following patterns:
oxoooo
oxxooo
oxxxoo
oxxxxo
One of these latter patterns (usually oxxooo or oxxxoo) will tend to approximate a C. However, if you try to use the same fingering to get a C in the second octave it probably won't work (a higher note tends to result as harmonics kick in) and closing only a single hole (oxoooo) may be a better solution.
Similar experimentation will usually lead you to a pattern which will
allow you to flat each of the highest three notes on a six-hole flute,
at least in the first octave.
Experimental results for one flute are as follows:
first octave second octave
C oxxooo
oxoooo
A# xoxxoo
xoxooo
G# xxoxxo
??????
(I ran into harmonics which prevented fork-fingering a second-octave
G# on this this flute.)
It's not usually practical to flat the lowest notes on a six-hole flute by the fork-fingering technique.
D oxxoxx (best) or oxxxxx
D# xxoxxx
E xxooxx (best) or xxooox
F xxxxxo
F# xoxxox (best) or xxxxox
G xoxoox (best) or xoxooo or ooxxxx
G# ooxooo or ooxoo?
A oxxxxx or oxxxxo
A# xxooxx or ???
B xDoooo or xoxoxo