The apostles don't even imply that. There is no mention of the word "reincarnation." You're just twisting the words and teasing out implications which are not even there.

First of all you must understand this, that no prophecy of scripture is a matter of one’s own interpretation - 1 Peter 1:20

And even IF they did, Christ definitively denies it by saying. Nope, that kinda thing never happened. BOOM!

As to "born again" even Nicodemus misunderstood and thought that born again was being physically born again.

Nicodemus said to him, “How can anyone be born after having grown old? Can one enter a second time into the mother’s womb and be born?” - John 3:14

Reincarnation is the same spirit being physically born again of different flesh which is just a variation of Nicodemus' misunderstanding. Christ is clear.

What is born of the flesh is flesh, and what is born of the Spirit is spirit. - John 3:6

Born again means spiritually renewed and the in-dwelling of the Holy Spirit and born again for the Kingdom of Heaven as Christians for 2000 years have always held. It is BAPTISM.

https://en.wikipedia.org/wiki/Baptismal_regeneration

Baptismal regeneration is the name given to doctrines held by major Christian denominations which maintain that salvation is intimately linked to the act of baptism, without necessarily holding that salvation is impossible apart from it. Etymologically, the term means "being born again" (regeneration, or rebirth) "through baptism" (baptismal).

Take that occult reincarnation hindu pagan garbage and put it back in the barn.