Webster 1913 says "a kite of infernal breed", perhaps bringing to mind a flying toy gone horribly wrong, a fighting kite of the worst kind, pursuing its hapless victims unto the death. But actually, this odd word utilizes a different, archaic meaning of the word kite: a person who preys on others. A kite, then, is a not very nice person, and a hellkite is even worse: a fiendishly cruel, wicked, nasty person. But not flying on the end of a string, and not swooping down from the skies to inflict wounds on the unwary.
Hellkite figures in that much-noded, but still (to me) supremely obscure...game? lifestyle? alternative universe? Magic: The Gathering, viz. Crimson Hellkite, Firestorm Hellkite, and Shivan Hellkite.