"action or habit of estimating as worthless," in popular smarty-pants use from c. 1963; attested 1741 (in a letter by William Shenstone, published 1769), a combination of four Latin words (flocci, nauci, nihili, pili) all signifying "at a small price" or "for nothing," which appeared together in a rule of the well-known Eton Latin Grammar + Latin-derived suffix -fication "making, causing."
[F]or whatever the world might esteem in poor Somervile, I really find, upon critical enquiry, that I loved him for nothing so much as his flocci-nauci-nihili-pili-fication of money. [Shenstone, letter, 1741]
The kind of jocular formation that was possible among educated men in Britain in those days. Just so, as in praesenti, the opening words of the mnemonic lines on conjugation in Lilley's 16c. Latin grammar, could stand alone as late as 19c. and be understood to mean "rudiments of Latin."