There is not one definitive fingering chart for the single-keyed flute. Flutes modelled after different makers will all vary in terms of bore size (thickness, width, etc.) and key hole spacing and size, which, when paired with the fact that no two players are the same, causes massive differences in intonation. This essentially means that a fingering that works for one player on a Palanca flute, won’t necessarily work for another player on a Palanca (much less another player on a J.H. Rottenburgh).
I have included several fingering charts, but the onus must be on you to figure out which fingerings work best for each note. Helpfully, many fingering charts are supplied with explanations on why certain fingerings may or may not work and what you can replace them with. It’s in your best interest to read through these explanations, as they can be really illuminating.
The first fingering chart is one supplied to me by Rachel Brown.
Below is Hotteterre’s fingering chart from Principes de la Flute Traversiere, de la Flute a Bec, et du Haut-bois (1728). When reading this chart, be aware that hole 7 represents the D♯ key, and when it is filled in, it means the hole is closed, therefore the key is not pressed; when it isn’t filled, the hole is open, therefore the key is pressed.
Next is Quantz’s chart from Veruch einter Anweisune die Flöte Traversiere zu Spielen (1752). It is for a two-keyed flute, but can generally be applied to the one-keyed flute if a specific fingering works for you.
Finally, I’ve included the fingering chart from Rudolph Tutz, a flute maker in Austria. Similar to the Hotteterre chart, when there is a black circle representing the key, do not press the key; when there is an X representing it, press the key; when there is a bracketed X, the key can be pressed or not, depending on your instrument.
I can also recommend Janice Dockendorff Boland’s book Method for the One-Keyed Flute as a good source for annotated fingering charts. Also, its quite difficult to find, but Margaret Neuhaus’s The Baroque Flute Fingering Book is a fantastic source (see the reading list for more detailed information on these).
Once you’ve sorted out the fingerings you’ll be using, remember to lift the fingers high enough away from the uncovered holes, because if they’re left hovering too closely, this can impact the pitch of the note. Also, move the fingers crisply to avoid any unwanted glides between notes.