Q: how do i get a refund of an in app purchase my kid made without permission?

You will have to contact iTunes Store support.

iTunes Store - Contact Us

If you have children using your device you really should set Restrictions especially for In-App purchases.

Settings > General > Restrictions > Enable Restrictions > set passcode > comfirm passcode > Turn off In-App Purchases

As Axeman suggested, you need to contact the iTunes Store, explain the situation, and request a refund. It's not guaranteed, but they're usually cooperative when it comes to inadvertent purchases made by children.

Regards.

I understand.

You will have to contact iTunes Store support.

iTunes Store - Contact Us

From what I have heard, they have been pretty lenient with In-App purchase refunds.

Developers can be pretty sneaky with In-App purchases.