While Webby is quite correct, there is another use of
sky pilot. One that was true even
when Webby walked the earth, but was low-down and dirty
slang so there's no way our illustrious Webby would include it.
In 1905, the Industrial Workers of the World was founded in Chicago. It was founded by socialists, anarchists, and all manner of people who were Just Plain No Good according to capitalism, but think of things like the conditions in The Jungle and the attraction becomes clear. The IWW, which was shortened slangily to 'the Wobblies' some time after, were vociferous in their preference for classless labor. They viewed the wage system as evil, and wanted elected representation at as many levels of the management chain as they could get so as to eliminate the difference between management and labor as a class barrier (I'm grossly oversimplifying this, natch).
In any case, as they organized events, causes and organizations to help the common worker, they often came into conflict with another large organization designed for charity - the Salvation Army. This other organization, being backed by religion, was anathema to many of the Wobblies, and as far as they were concerned, the Salvation Army was intended to 'pacify' the laboring class to perpetuate the evils of capitalism. One of the primary modes of expression of the Wobblies was in song; and in 1911, the famous Joe Hill wrote a song titled The Preacher and the Slave (set to the tune of the Salvation Army hymn In The Sweet By and By) to emphasize that the latter group was just mouthpieces for management and the capitalists.
In that song, he put the line: "Work and pray, live on hay, you'll get pie in the sky when you die."
This, natch, is the origin (I think?) of the phrase pie in the sky. However, it was coopted for the term "sky pilot" - which was used by Wobblies to describe priests or preachers who were tools of the management and who counseled tolerance and acceptance of the status quo.
There are only two other groups at that time who relied as heavily on song to get by, probably - and those are convicts and the military. Sure enough, the U.S. military began to use the term "sky pilot" to refer to official service chaplains - in some of their view, fulfilling the same role as the 'sky pilots' of the Salvation Army; there to soothe the rankers into accepting the injustices heaped on them by the management (officer) class.
As folks began to cycle through the military and back out into civilian life, the slang term 'sky pilot' for a preacher went with them. Eventually, at the attack on Pearl Harbor at the outset (for the U.S.) of World War II, a sky pilot would become famous (perhaps injustly) - and be called one in song designed to whip up patriotic fervor.
Contrary evidence
Of course, nothing's certain. Cassell's dictionary of slang, the representative page of which is available on google books, lists sky pilot as being 'late 19th century' in origin. It does, however, state that it refers to a prison chaplain, or a preacher or missionary, which jibes with the above history of the term. That dictionary, however, was published originally in 1998, so it, too, is reasoning after the fact along with us.
Since the job of a pilot is to help a vessel negotiate treacherous and unfamiliar waters in order to reach a port, perhaps priests were seen as performing pilotage duties for souls seeking heaven - hence, pilot of the sky.