I am not quite sure what the original question is here, but the boy in that painting is clearly playing a transverse flute. But then again, he doesn't look like a peasant boy, in fact he looks quite upper-class to me. Speaking generally, apparently the transverse flute was especially associated with Germany. To quote from the book Instruments of the Middle Ages and Renaissance by David Munrow: "The instrument [the transverse flute] became something of a German speciality and the expression German flute is found off and on for the next 800 years as a means of distinguishing the transverse flute from whistle types". That is a quote from the section about the middle ages. To quote from the section on the renaissance: "the transverse flute was especially cultivated in Germany in medieval times and became known as the flûte d'Allemaigne during the Renaissance".

On the other hand, as Malcolm says, a simple recorder type instrument or tabor pipe is probably more likely for a peasant boy. These instruments were certainly not unknown in Germany. And the transverse flute of that era was apparently very difficult to play.

(Disclaimer: I don't really know anything about it. I just found some stuff in a book.)