Haven't you answered your own question here? Recorder.

Actually, my edition of these pieces says that it is the recorder player who has nicked the flute music, again...

My book says that the recorder edition was produced from a research publication of Telemann's chamber works without bass, and that, as was conventional in Telemann's day, most of the pieces had to be transposed up a minor third to fit the treble recorder, except for three, which were put up a fourth. I don't know if the Fantasias were published originally in the magazine called "Der Getreue Musikmeister" - a publication which allowed people to get ready access to new music from which to learn.
Sorry not to have been of more help!