Is there a hadith that prohibits eating the skins of birds?

There is no Hadith that prohibits eating the skins of birds or other animals whose meat is permissible to eat. Jurists have permitted eating the skin of an animal that has been slaughtered according to Islamic law. As for the skin of a dead animal (carrion), it is not permissible to eat it, whether before or after tanning, due to Allah Almighty's saying: ﴿Forbidden to you are carrion﴾ and due to the Prophet, peace and blessings be upon him, saying: "What is forbidden from carrion is only its flesh." And skin is a part of carrion, so eating it is forbidden.