(noun) type of flying toy
The use of this word to describe the colourful, soaring child's toy is not recorded in English until 1664.
Before that, the only usage was to the hovering bird of prey - and this is the sense we find in Shakespeare.
When Cassius remarks that "ravens, crows, and kites Fly o'er our heads"
(Julius Caesar, V.i.84), we must not let the modern meaning interfere.
The kite was perceived to be a bird of ill omen: when they were around, things were not going well.
Macbeth says to his wife that their monuments "Shall be the maws (stomachs) of kites" (Macbeth, III.iv.72).
Pistol calls a whore "a lazar kite" - that is, a leprous bird (Henry V, II.i.73).
Petruchio talks about kites "That bate (beat the wings) and beat and will not be obedient" (The Taming of the Shrew, IV.i.181).
So it is not surprising to find the name being used as a term of abuse.
"Detested kite", says Lear to Gonerill (King Lear, I.iv.259).