Before the owl can repair your wing, it wants the egg from the nest in the next tree. You can’t fly but have to figure it out otherwise the owl won’t help you.
Walk to the left of the tree. Pick up the GLOVE. Go inside the tree again and talk to the owl. Give the glove to the owl and now you’re alowed to take the SCISSORS and the CAPE. Use the scissors on the cape to cut it into a rope and leave the tree house.
Walk to the right side and from the branch you can see the nest. Use the rope on the nest to get a walking rope to the other tree. Use the scissors on the rope again to secure it on your end. Now walk the rope to the other tree and take the EGG from the nest. Walk back to the left, enter the tree house and give the egg to Augustus.
Tell Augustus your concern about stealing the egg and he’ll return it, helping you with the wing anyway.
Game source: A copy of the game was found here on the internet.