I've already replied to this but computer crashed...
Thanks to all for the scans/emails/links to the King.
I did some digging and Sylphs seem to be associated with the wind but there is some disagreement if they are elementals which are seen as different to pure fae.
If they are elementals, this is a hybrid of different thought at the time the deck was produced:
""Occultist" or "mystical" folklorists like Yeats and Evans-Wentz (both of whom were believers) sought to philosophically reconcile the elementals and the supernatural creatures of folklore. They inquired, through informants, about traits common to both popular fairies and elemental spirits, and they sought to locate the ways in which the various orders of beings had merged. AE (George William Russell) believed, for example, that the lower orders of the sidhe were the elementals seen by the medieval mystics."
http://www.nytimes.com/books/first/s/silver-strange.html
It was commonly believed at the time that fairies were uncommitted angels or those trapped on earth during Lucifer's fall. Equally widespread was the view that the fairies were the souls of the dead who were not good enough for salvation or evil enough for damnation. It was also believed that fairies were the spirits of unbaptized children or that they were spirits of "special" categories of the dead, those awaiting reincarnation, or those killed before their time, or those from long-dead, pagan, or extinct races.
I have found references to Sylphs from both Crowley and Levi. In The Conjuration of the Four Elements, Levi talks of elementals being like poltergeists and naughty children:
http://www.propheticmystic.com/Teachings/Elementals/Elementals2.html?height=600&width=900
He cites the prayer of the Sylphs which Crowely also cites in Liber T and other documents. He also talks about Undines. I think that the Sylphs are a mixture of Victorian Spiritualists, Rosicrucians, and Theosophists' and are mischevious spirits or subhuman elves. Levi talks of conjuring them up and using them for magical purposes.
Leadbeater describes nature spirits, including gnomes, fairies, undines, sylphs, and elementals, as the aboriginal peoples: "the original inhabitants of the country, driven away from some parts of it by the invasion of man" (p. 84). Paralleling the upward spiritual evolution of man (from an ordinary half-evolved state through stages as "Advanced Man," "Disciple," and finally "Adept"), fairies also evolve, becoming sylphs, devas (or angels), and ultimately higher angels.
http://leadbeater.org/tillettcwlappendix1.htm
So on parallel to Adepts, Disciples and Men, Leadbeater has Devas, Sylphs, Cloud Spirits, Water Spirits, Salamanders and Land Fairies.
So it seems as though the King of Swords is turning his back on anything that may try to distract him, and since Sylphs are associated with the Wind and later Air, they would move as quickly as the wind and he doesn't want to change his mind. They are also mischevious and may try and lead him down the wrong road or trick him. He may also be turning away from fantasies or whimsies.