I actually learned this from a 10,000 Maniacs song (`Katrina's Fair'). It has a line:
Sylvia keeps beasts in jars
Label them by their kingdom phylum order class
Family
Genus species
You see the problem... Ms Merchant swapped `order' and `class' to get it to scan (in the lyrics sheet it is listed as class order). In any event, I somehow remembered the hierarchy better when it was set to music, even if I had to remember to swap order and class.

Not that that's a mnemonic. How about:

Killer Penguins Crawl On Frozen Glacial Shores
Kirk Punches Chekov On Face, Getting Stares
Kant Provides Crazy Ontology For Graduate Students
Knotted Penises Caress Only Flexible G-Spots