Is there really good evidence that James Leininger was reincarnated....?

It depends on what you consider good evidence. There certainly is no evidence good enough to erase any doubt.

Depends on what "Good" evidence is---It is certainly Suggestive of reincarnation.  Indeed similar "evidence" can be found in many different cases.  However, it is the only evidence we have for it.------We have even LESS evidence for other "afterlife".----So if there is ANY evidence of afterlife--it points to reincarnation.----  

Most religions have "loopholes" or "hidden" teachings where reincarnation happens or is an occasional thing --at least sometimes.  Even Christianity, in the Bible suggests it happens sometimes. John the Baptist, was said to be the reincarnation of Elisa and revelations says he we be again reborn as a prophet in the end times.

The Jesus Scenario appears to be taken from Eastern Spiritual Philosophy, with his  taking on of our "Sin-Debt"---also known as "Karma" so we may be "pure" or "perfected enough" to join him and God on the higher "god planes" when we die.   A somewhat simplified version of the Eastern Karma thing, where we must be reborn over again to "work off" our Karma to eventually Join God on the higher God planes.--Breaking the reincarnation cycle.  Along with the Guru or "Teacher" who has the ability to take on individual Student's Karma" himself, to help his pupil along.------

Only JESUS ups it one better and will take on everybody's KARMA (but you gotta ask first)  ---And they leave out the part that you might be reborn many times before then.

As a Methodist I usually accept the general Jesus removing the sin debt thing allowing me to join him and God in "heaven"  and not being subject to the default "realm of the dead"  translated as "Hell" (from "Hel", the Nordic rip-off of the Greek Hades)-----I could ALSO believe in Reincarnation also, with no conflicts, as it's just Christianity "with a little more information." ---depends on how you interpret the Bible.---it does not say it specifically, but hints at it in places and says it happens sometimes.

Personally, I HOPE there is NO Reincarnation---I am happy how THIS life turned out and would hate to have to start ALL over again.  

I was impressed by the little kid who claimed he was on the Titanic---and kept drawing pictures of it sinking (Before the movie came out)----The kid even included the "Docking Bridge" near the stern---something I was not even aware of until I  was working on a model of it.----How many adults even know what a docking bridge is?---much less a kid .

"At the age of three, James began to draw. What he drew were always about planes and battles. He named the planes of his drawings – Wildcats and Corsairs. He called the Japanese planes Zekes or Bettys. When asked why these names, he said that “The boy planes were fighters and the girl planes were bombers.” Bruce checked this in the internet and again James was right."

https://www.reincarnation-research.com/james-leini...

I assume we're talking about a boy who couldn't read at age three. Where did he get that?

The title of the Skeptoid article is a misnomer. It's about reincarnation stories in general and says very little about this particular case.

It doesn't seem that the parents were engaged in wishful thinking, They are described as Christians - people whose religion does not promote belief in reincarnation.

Perhaps in any discussion where "truth" is in question, one does well to first set clear definitions of what "truth" may be for a given area.  Obviously, if you're baking a cake, the proof is in the eating.  If you're constructing a building, the proof is if it stays up, functions as designed, etc.  If you're constructing a physics hypothesis, the proof will be in the experiments which confirm the hypothesis.  If you're talking about God, reincarnation, etc., generally it is foolish to take a yardstick to measure God, look for a golden birth certificate, etc.  In the area of reincarnation, the more "truthful" or convincing accounts are simply more tenuous than more physical proofs.

Some of the better reasons for entertaining the Leininger account:  in the parents' account, they begin as one-life Christians who are skeptical of their very young son's unusual "memories" and strong feelings.  They have to be convinced by the "evidence."  The therapist they contacted, via learning of her via her book, gave some therapeutic advice that promoted a "your dreams reflect your reality" perspective.  What the skeptoid omits in his outrage is that the specific information about the specific plane was not available nor made available to the child--not by tv, nor any other means.  Likewise, the meeting with his former wing-mates is not mentioned by the skeptoid.  The skepticism of the father is also not addressed by the skeptoid.  This is the problem with bigoted approaches to the God, reincarnation type(s) of truth-claims--a biased or one-sided cherry-picking of only "human influences" events is simply that--biased, prejudging, and not helpful to genuine examination of this kind of event.  The most telling point is that Corsairs were not flown off the USS Natoma Bay.  This indicates that there was at best some conflation by the child, but does not by itself negate the general narrative of a child with some possible strong memories of WWII service.  Here is another perspective with more evidential truth-claims:  https://psi-encyclopedia.spr.ac.uk/articles/james-... which ought be subject to the same standards of consideration as the skeptoid article.  The skeptoid does not report the photo of James Huston, kept by his sister, Anne Barron, showing him standing by a Corsair, nor statements made to Anne Barron by the child about specific family details, the child's naming of his favorite action figures Billie, Walter, and Leon, who were three squadron-mates of James Huston who'd died before James Huston died, and who were helping and welcoming him into the heavenlies where the child stayed between incarnations.  In other words, a very biased skeptoid article which leaves out what the above-cited article includes is at best a biased argument, even to the ad hominem slurs the writer uses.  The emotion on this general God, reincarnation issue-set is not limited to wishful thinking on the part of pro-reincarnation people, but also shows as hatred and illogical atheism on the part of so-called "skeptics."

Some of the evidence is young Leininger's specific, repeated, and accurate knowledge of specific types of WWII aircraft; and his recognition of wing-mates at one of their gatherings.  Imo, it is a distinct psychological process whereby the young child would tend to prefer to identify the Corsair which he'd flown, rather than the more fire-ball-horror FM2 Wildcat he'd tragically and allegedly died in.

There is no "who benefits" for the Leiningers writing and publishing their account.  They are essentially trying to help other parents and their rather unique children.

So, it is not possible to bake the reincarnation cake, build the reincarnation building, etc., but that is to be expected going in.

Some similarly "convincing" accounts include "The Reincarnation of Edgar Cayce?" by Free and Wilcock;

"Autobiography of a Yogi" by Paramhansa Yogananda; and Dr. Jim Tucker's (and Dr. Ian Stevenson's) books, "Return to Life" and "Life before Life."

It is illogical to deny either God and/or reincarnation, as that's claiming you've proven a transcendental negative.  Likewise, the claim for God is usually the Kingdom within a la Elijah, and the claim for reincarnation is some awareness or even memory that is not otherwise accountable for.  As for your leading question, "Is it more likely...", that is obviously not a question which can be answered in either direction, although your insinuation of greed and wishful thinking is again somewhat an ad hominem, rather than a sincere approach to a difficult type of truth-claim evidence.  Bias and emotion, negative or positive, when investigating truth-claims, is a fallacy ab initio.  Certainly it is incorrect to characterize Mr. Bruce Leininger's attitude for many months if not years as "wishful thinking."  It is well to note that there is a bell curve of people who are able to tolerate ambiguity.  Black and white fallacies tend to emerge from those who prefer to have neat answers, even in areas where "all doubt" cannot be removed (this "all doubt removed" perspective results at best, when carried to its extreme of solipsistic questioning, in Hume-type denial that we may know anything).

 No none whatsoever

Yes you're correct and the Lord Jesus Christ is not God.