The transverse flute was certainly known in Germany during the 16th century, so far as I know without keys and with smaller finger holes than we have today. End-blown flutes such as the recorder were still much more popular at that time. A peasant boy might perhaps have been more likely to play a form of "rustic flute" (more or less a home-made whistle) or the three-hole pipe (as in "pipe and tabor").

Not my subject, mind; but if we keep the thread current, people who know more will be along in time.