I believe in reincarnation. It doesn't go hand and hand with physics, and I am not entirely sure if there is a place spirit energy based entities go when they pass on, but the transformation of energy is indeed true. Energy changes and is never destroyed. Well, rarely.
If we are to argue that a soul being some form of energy, the argument that energy changes states would actually go against reincarnation. For these memories and such of past lives to continue on that energy would have to remain unchanged to a certain degree.
As for the story. We would really need more details to truly debunk it. The first thing that would have to be ruled out would be if the parties involved are simply lying. but let's grant them that they aren't lying.
Further research on the story reveals this video is actually leaving out an important detail. His fascination with WWII and planes started at 18 months old when he was taken to an air museum and spend 3 hours in the WWII exhibit. It was after that these nightmares and such started. It's quite likely with such an obsession he would have managed to pick up all sorts of details along the way.
As such we would then have to find a way to rule out the possibility that he simply found these details without the parents knowledge and is running on false memories created from this information. Again I'm not saying this is the case, I'm simply saying this is just one more point that would have to be investigated an eliminated before we can start entertaining the notion of reincarnation. We would also have to ask why it would only start after being introduced to a museum exhibit.
Now after this obsession started with James his grandmother suggests he go to a therapist who then encouraged James to share his memories.
This suggests that James could have been either deliberately or unintentionally manipulated into having false memories of WWII events.
As the reincarnation idea becomes more ingrained a couple of people who have written books on the matter are brought in. At least one of which (Ian Stevenson) is known for asking leading question to youths. (Leading Questions: try to lead the respondent to your way of thinking.) This would seem to only further suggest the possibility of the existence of false memories based on true information that the boy was exposed to.
Now about his hits . (the points he got right)
Signing his name "James 3"
This one is not surprising given he had recently turned 3 years old at the time he started doing that. It would be a bit more interesting if he was signing the name "James III", but not by much.
Getting specific names. Given the likely hood James has either been intentionally or inadvertent lead on at this point, we really can't say much of anything. Did he really at first say this or was it something that was just similar?
Could he have picked up any of these details some place and the parties involved simply don't remember him doing so, or the parents are just mus-remembering events as well?
Could we also have a case of confirmation bias, where the parties involved are only remembering the hits James has gotten over the years but are forgetting all the misses? Of course given the nature of the way the story was told in the video any such misses would have likely been left out.
So would I call this debunked? No. Would I call this compelling evidence for reincarnation? No.