Hi Serge,  I too am the owner of a Black Forest flute clock from around
1805.  It's now in a playable state although I was forced to mute the
open pipes and only use the 'Gedacht' pipes.

First of all, you must get all available literature on the subject.
I can strongly recommend the book by Herbert Jüttemann: Schwarzwälder
Flötenuhren, Waldkircher Verlag 1991, ISBN 3-87885-236-3.  The book is
in German and has great emphasis on the musical part (the organ works)
of the flute clock.

Good luck with the job!

Peter Heinesen
http://www.peter-heinesen.dk/