I find the attempt to harmonize the theory/law of Karma with Christianity to be of little benefit, and possibly dangerous. I can only imagine that Christians who would do so are doing it from an ignorance of what the principles of Karma are, and are unknowingly practicing a form of syncretism - and that's the best case scenario. Worst case, they end up traveling into the realm of heresy.
Surely we are knowledgeable enough as Christians to understand that reincarnation is not Biblical. So before we can even attempt to integrate Karma into Christianity we have to throw away that major part of it. But there are other problems with Karma other than the reincarnation bit. The general idea of Karma is that our actions create some sort of invisible metaphysical "pool" of either good karma or bad karma, and those "pools" have power and influence over our future experiences. Thus, people who do more good and are able to accumulate good karma will have better things happen to them in the future, and vice versa.
The problem is that the underlying principle of Karma is also not Biblical. Consider Job. Job was an upright and righteous man. Karma would not be able to explain what happened to him. Consider all of the Apostles who were martyred for their faith. Surely devoting one's life to Christ and sharing the Gospel would have generated the greatest amount of karma - yet they were all persecuted, abused, and ultimately killed for their faith.
The stark reality of Scripture is that we exist to glorify God. We aren't promised happiness, wealth, or good results from our behavior. We are actually warned that to be followers of Christ makes us enemies of the world. The entire meta-narrative of Christianity stands diametrically opposed to the meta-narratives of the eastern religions that embrace the concept of Karma.
There is no good or beneficial reason for Christians to attempt to adopt Karma into our worldview. The principles of karma - its foundation - is incompatible with Christianity.
Following from that, the previous comments about how children perform a form of Astral Projection when they call themselves Batman or Superman is utterly absurd and shows a complete ignorance to what Astral Projection actually teaches.
The general idea of Astral Projection is that a person, either consciously or sub-consciously creates an out of body experience where they essentially leave their physical body and are capable of traveling through the world/universe in their Astral Body (or soul). This is so far away from what my 5 year old son does when he runs around the living room saying he's Superman. I can only imagine that the person who would compare these two is either totally ignorant to what Astral Projection really is, or they have no children. Though both is probably the more likely case.