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That's just a 10 second commercial. Not it at all.
I remembered seeing this years ago. I read this query a few days ago and I tried searching the web, but no luck.
Today I read this again and I suddenly remembered the title. It's called The Itch and I was able to find it. You can find it yourself by searching for "The Itch 1965".
Edited by FerrousFaucetThank you Ferrous Faucet! Thank you so much!
I think this cartoon was from a series of shorts Nickelodeon did in the late 80s/early 90s. There was a man and he had an itchy back, so he scratched it against his chair and he grew wings. He spends the cartoon flying around until his wings get shot off. He's all depressed, then notices something poking out of his jacket. He smiles, scratches his back against the chair again and gets his wings back.