Fillip

v. To flick one’s finger (or the act of doing so), by bracing it against and snapping it away from the thumb, often euphemism or simile for encouragement

This may be a dismissive gesture, be used to indicate a direction, or to discard probuscine effluvium

Examples:

If I do, fillip me with a three-man beetle.
— Falstaff, Henry IV part 2, by William Shakespeare (1599)

Eat, drink, and love; the rest’s not worth a fillip.
— Lord Byron, Sardanapalus (1821)

Faithful horoscope-watching, practiced daily, provides just the sort of small but warm and infinitely reassuring fillip that gets matters off to a spirited start.
— Shana Alexander, “A delicious appeal to unreason” (2005)

Etymology: Appearing in the 15th century, it seems simply to remind one of the sound that the gesture would make