Purchases are linked to the account that made them and can’t be shared between profiles. Follow these steps to restore purchases made with the same Amazon FreeTime account: 

1.    Launch the FreeTime app

2.    Switch the account to the FreeTime account that is linked to your purchase.

3.    Launch the app and let it download completely.

4.    Enter the in-app Settings Menu.

5.    Tap on Restore Purchases (from the child’s FreeTime profile).

All purchase made with that same FreeTime account should immediately restore.