Since human beings have an innate desire to eliminate injustice where possible, Institutions are not that important.

Yeah, sure. That is why the entire world is based on injustices.
Stupid people getting rich, while the hard worker people remain poor, and so on.

Should CHILD B Get the Flute?

If he really made the flute, then yes. I would bring the flute back to CHILD B. If he keeps it, or he sell it to someone else, then that is his rightful decision. The flute belongs to him. He owns it.

Easy and obvious.