I don't know if it was "plagiarized" in the full meaning of the word, but it definitely wasn't his. He took the idea from somebody else and let the public think it was his own original thinking.
Also, we keep reading about how handsome he was. Maybe I'm the only one; but for me, he was ugly.
Reports from years ago indicated that that part of the speech was the motto of his prep school, Choate, as in "Ask not what Choate can do for you. Ask what you can do for Choate."
I've seen no confirmation and I doubt that Choate would admit it.