Rockstro was no fan of what he called "pseudo
old-fingering-flutes" - flutes that generally finger like an 8-key flute
in the lowest and second octaves, but which have keys added to relocate
some holes (eg the Siccama flute), or which rely on Boehm's bore but not
his keywork. But he kindly provided a list of fingerings that can be
helpful in the third octave, where these flutes tend to depart
significantly from standard 8-key fingering. The table below is
lifted from Rockstro's Treatise on the Flute.
You will see I rarely go up that high myself, and have had
to pencil in the names of the notes to save having to count the ledger
lines. I've left them in just in case you suffer from vertigo too!
There are several fingering charts for the usual 8-key
flute elsewhere on this web page. These can be used for the first
two octaves of pseudo old-system flutes.