Every flute is different. Choose the fingerings that work best on your instrument, after making a serious attempt to understand those recommended in 18th century sources. I recommend The Baroque Flute Fingering Book by Margaret Newhaus, which contains a compilation of trill fingerings from many 18th century sources.
We give mostly fingerings for baroque flutes and pre-classical types. They will work on later classical and 19th century one-key flutes as well, but some may not have been used—for reasons of style—in the 19th century. Some of the fingerings suggested are not to be found, exactly, in 18th century sources.
Trills (and other ornaments) are immensely important in 18th century music. The trills on a baroque flute are one of its charms. Many work better than trills on a modern flute, in part because the sound of a smallish hole being opened and closed relatively quickly by a finger seems smoother (less clicky or mechanical sounding) than that of a large hole being opened and closed by a key pad, and also because the lack of mechanism means that they can be done more effortlessly—and the appearance of effortlessness is essential. Trills should not be mechanical; they should flatter the ear. Don't be afraid to vary dynamics, timbre, and speed while a trill is in progress, when time permits.
It has been said that some trills on the one-key flute are "out of tune". Mind you, they should not impress a listener as being out of tune; it is the player's job to hide any inherent out-of-tuneness. The gesture is more important than exact intonation according to equal temperament, say, and the ear can be surprisingly flexible and can actually enjoy expressive playing with intonation. I once heard a professional violinist say that at first she, with her trained ear, didn't appreciate the wide trills (see below) on baroque flute, but that she came to like them with time, and since then tries to imitate them on the baroque violin.
Trills always begin with an appoggiatura, usually the note above the main note (the upper auxilliary); they should often (some would say always) end with a turn, consisting of the note below the main note (the lower auxilliary) and the main note again. The following is from E. R. Reilly's translation of Quantz' Versuch of 1752 (Chapter IX, Section 7).
The 'trill proper' will often use a fingering chosen for ease of execution, and not one that that is simply the alteration of the normal fingers of the upper auxilliary and the main note. After the appoggiatura, one switches to the 'trill fingering', and one hears first the main note. So one can practice the trill fingering starting on the main note, as shown in Quantz (Chapter IX, Section 6):
It is important to keep the main note at the same pitch as the normal fingering, but often the upper auxilliary does not exactly match the normal fingering in pitch or tone. It is sometimes possible to find a trill fingerings where the interval between the upper auxilliary and the main note is a bit wide (the upper auxilliary is sharper than it should be) and another where the interval is a bit narrow (the upper auxilliary is flatter than it should be). In such a case, the baroque flutist almost invariably chose the wide trill fingering, according to the surviving sources. This gives a lively and clear trill, as opposed to a wobble. These wide trills can better be heard through other instruments and in an orchestra.Examples:
It should be remarked that fingerings used in slow movements may differ from those in fast movements. Just as the fingering for g''b may be used for f''# between an e''# and g''#, so the a''b over g''b trill fingering may be used for g''# over f''# in a slow movement (where one has time to adjust the intonation).