I once had a library book about the paintings of a 17th-C Dutch painter named Judith somebody. She did a painting of a young boy from a family of entertainers, and he was holding a recorder or flageolet, which are both flutes which you play up and down, not transverse flutes.

The boy had been playing in a tavern. He did not look healthy, and I felt that she was applying a mother's eye to the scene.

Anyhow, your story will be more credible if the flute is not transverse and if the boy comes from a family of performers.

I believe that the wooden transverse flute was just coming to its own in the 17th C because it has a conical bore. This means that the hole inside it tapers from wide to narrow as it goes down. Cutting that out was a pretty sophisticated task. I doubt if a commoner, especially a child, could have afforded one.