Directly from the Bible we see that John came in the spirit of Elijah. John was not literally Elijah and no Jew hearing Jesus say "he (John) himself is Elijah" would have thought Jesus was suggesting Elijah had been reincarnated. Reincarnation is just not an idea in the Bible and neither is Karma in the strictest sense of the word.
"Do not be afraid, Zacharias, for your petition has been heard, and your wife Elizabeth will bear you a son, and you will give him the name John. 14"And you will have joy and gladness, and many will rejoice at his birth. 15"For he will be great in the sight of the Lord, and he will drink no wine or liquor; and he will be filled with the Holy Spirit, while yet in his mother’s womb. 16"And he will turn back many of the sons of Israel to the Lord their God. 17"And it is he who will go as a forerunner before Him in the spirit and power of Elijah, to turn the hearts of the fathers back to the children, and the disobedient to the attitude of the righteous; so as to make ready a people prepared for the Lord," (Luke 1:13-17).
Are you a Seinfeld fan? In the episode "The Fire" Kramer tells a story about driving a city bus while fighting criminals and making all the required stops.
George exclaims, "You're Batman!"
Kramer agrees, "Yeah, I am Batman."
Neither character thought that Kramer was actually the superhero Batman. He was doing things that Batman would have done. Often language uses colloquialisms and therefore cannot always be taken literally.