Rennaissance flutes were indeed cylindrical and one-piece. They were made in a range of sizes from descant down to bass, with the tenor flute corresponding to the D flute we know today. They did not have decorative turnings. I've seen the range given as two octaves and a sixth--that's really stretching it, as two octaves was about the usable range. The upper end of the second octave used vented partials as the overblown fundamental was too far off pitch due to the cylindrical bore.
Early Baroque flutes introduced the conical bore and multi-piece construction. Some of the earliest were made in 3 pieces (similar to our "Pratten" Irish flutes) with a single key for E-flat. Later 4 part construction was introduced, adding an adjustable break between the left and right hands, and a second key was added, for D-sharp. The baroque flute had a usable range of almost three chromatic octaves. The decorative turnings were an evolution of the swellings added to the joints to strengthen them.
The flute pictured in this thread doesn't resemble any Rennaissance or Baroque flute I've ever seen.
You can see pictures of reproductions of early flutes at
http://www.baroqueflute.com/
--James
