Please explain how you match up "Mystery of Iniquity" with reincarnation. That phrase only occurs once in the Bible, in 1 Tessalonians 2:7 :Like I said earlier, the term for the Biblical form of Reincarnation is 'Mystery of Iniquity' as well as 'Was, is not, and yet is'. I suppose we can throw 'Child of Hell' in there as well.
"For the mystery of iniquity doth already work: only he who now letteth will let, until he be taken out of the way." (KJV)
"For the mystery of lawlessness already works. Only there is one who restrains now, until he is taken out of the way." (WEB)
It's from a passage where the apostle Paul is explaining that "the day of Christ" has not already come. Here's the full passage (WEB):
1) Now, brothers, concerning the coming of our Lord Jesus Christ, and our gathering together to him, we ask you
2) not to be quickly shaken in your mind, and not be troubled, either by spirit, or by word, or by letter as if from us, saying that the day of Christ has already come.
3) Let no one deceive you in any way. For it will not be, unless the rebellion comes first, and the man of sin is revealed, the son of destruction,
4) he who opposes and exalts himself against all that is called God or that is worshiped; so that he sits as God in the temple of God, setting himself up as God.
5) Don’t you remember that, when I was still with you, I told you these things?
6) Now you know what is restraining him, to the end that he may be revealed in his own season.
7) For the mystery of lawlessness already works. Only there is one who restrains now, until he is taken out of the way.
8) Then the lawless one will be revealed, whom the Lord will kill with the breath of his mouth, and destroy by the manifestation of his coming;
9) even he whose coming is according to the working of Satan with all power and signs and lying wonders,
10) and with all deception of wickedness for those who are being lost, because they didn’t receive the love of the truth, that they might be saved.
So the "Mystery of Iniquity" is referring to "the man of sin" who will be a servant of Satan and will perform "signs and lying wonders" to deceive all non-Christains, because they "didn’t receive the love of the truth". It has absolutely nothing to do with reincarnation.
Regarding "Was, is not, and yet is", that is a quote from Rev 17:8 :
"The beast that thou sawest was, and is not; and shall ascend out of the bottomless pit, and go into perdition: and they that dwell on the earth shall wonder, whose names were not written in the book of life from the foundation of the world, when they behold the beast that was, and is not, and yet is."
The book of Revelation is full of symbols, and the angel explains the meaning of the symbols of the beast:
7) The angel said to me, “Why do you wonder? I will tell you the mystery of the woman, and of the beast that carries her, which has the seven heads and the ten horns.
9) Here is the mind that has wisdom. The seven heads are seven mountains [kingdoms] on which the woman sits.
10) They are seven kings. Five have fallen, the one is, the other has not yet come. When he comes, he must continue a little while.
12) The ten horns that you saw are ten kings who have received no kingdom as yet, but they receive authority as kings, with the beast, for one hour.
14) These will war against the Lamb, and the Lamb will overcome them, for he is Lord of lords, and King of kings, and those who are with him are called chosen and faithful.”
And so on. The beast is therefore symbolic of kings and kingdoms, past, present and future. It too has nothing to do with reincarnation.
Finally your reference to "child of hell", which is a quote from Mat 23:15 :
"Woe unto you, scribes and Pharisees, hypocrites! for ye compass sea and land to make one proselyte, and when he is made, ye make him twofold more the child of hell than yourselves."
To be a child of hell was a Hebrew phrase, signifying to be deserving of hell, to be awfully wicked.
Here Jesus is admonishing the scribes and Pharisees "For they bind heavy burdens that are grievous to be borne, and lay them on men’s shoulders; but they themselves will not lift a finger to help them" (Mat 23:4). “But woe to you, scribes and Pharisees, hypocrites! Because you shut up the Kingdom of Heaven against men; for you don’t enter in yourselves, neither do you allow those who are entering in to enter" (Mat 23:14). Jesus is saying that although they spare no effort to convert someone to Judaism, yet by there false teachings they are preventing people from entering the Kingdom of Heaven, and they end up making those converts doubly deserving of hell than the Pharisees themselves.
Barnes Notes says:
The Jewish writers themselves say that the proselytes were "scabs of Israel," and "hindered the coming of the Messiah" by their great wickedness. The Pharisees gained them either to swell their numbers, or to make gain by extorting their money under various pretences; and when they had accomplished that, they took no pains to instruct them, or to restrain them. They had renounced their superstitions, which had before somewhat restrained them. The Pharisees had given them no religion in its place to restrain them, and they were consequently left to the full indulgence of their vices.
So once again, it has nothing to do with reincarnation.