Duquette says that the knight's wings are fixed to his back, not his helmet, and that seems correct. I always thought that they're on the helmet
There are a number of reasons why dragonfly wings seem a good choice for the suit of Swords. They are geometrical, transparent and lend themselves to abstraction and stylization.
Dragonflies, as opposed to birds, undergo transformation - they are not born with wings but acquire them.
Besides, by using dragonfly patterned wings, Harris avoids the association with angels (human figures with bird wings) or mythological Psyche (butterfly wings).
Here is the Duquette quotation (n.b. that dragonflies have four wings - and that's what Harris paints):
Beginning with the Knight of Swords, we see that what appear at first to be four propeller blades spinning atop his pointed helmet are actually four triangular wings sprouting from his back. They are transparent and veined, like those of a dragonfly. Perhaps there are only two wings that are moving so fast they appear as four. Please take a moment and look at the Queen, Prince, and Princess of Swords, and locate the marvelous angular wings on these figures. Now look at all the small cards of the suit and see the backgrounds festooned with these stylized wings— some balanced, almost pinwheel in form; some twisted, broken, stretched, and distorted.
DuQuette, Lon Milo (2003-11-15). Understanding Aleister Crowley's Thoth Tarot (p. 190). Red Wheel Weiser. Kindle Edition.
Does anybody see wings on the queen card? I didn't.