The phrase to flay a fox occurs many times in English translations of Rabelais. According to many sources, it means to vomit.
These and other sources also mention the variant to flea a fox.
Further, Partridge mentions whip the cat as an alternative (although I'm dubious given that whip the cat seems to have a completely independent meaning).
Here are some examples of flay the fox in Rabelais:
At the time of the paroxysm he used to flay a fox by way of antidote.
(Pantagruel Book 4, Ch. 44)
The definition meaning "to vomit" is corroborated by the above passage, as well as by the following passage, where a link is presumably drawn between flaying foxes and vomiting:
And all those fine folk were soon puking in front of everyone else as though they had been flaying foxes.
(Pantagruel Book 1, Ch. 12)
This passage suggests that the origin of the phrase comes from the actual practice of flaying (that is, peeling the skin off of) foxes, a presumably vomit-inducing activity. I've noticed that some translators of Rabelais actually use "skin the fox" over "flay the fox," suggesting removal of skin as the practice which originated the phrase.
But I am perplexed by the following passage, where it is not immediately obvious that flay the fox means "vomit":
With this he took him by the throat, saying to him, Thou flayest the Latin; by St. John, I will make thee flay the fox, for I will now flay thee alive.
(Pantagruel Book 1, Ch. 6)
Further, Partridge's listing of whip the cat as an alternative suggests that flay should be understood as "whip", rather than "peeling the skin off of", contradicting the above folk etymology. Further, we have many animal-beating idioms which, on analogy, suggests the "whip" etymology over the "peeling the skin off of" etymology. For example flogging the monkey and beating a dead horse.
(1) Peel the skin off (a corpse or carcass):
(2) Whip or beat (someone) so harshly as to remove their skin
By googling I have also found a rather intriguing definition which reads:
flay (or flay the fox), verb, phr. (old). To vomit: "from the subject to the effect," says Cotgrave; "for the flaying of so stinking a beast is like enough to make them spue that feel."
This suggests that to flay, more generally, can mean to vomit. It also corroborates the "removal of skin" folk etymology that I gave. Presumably "Cotgrave" refers to this Dictionarie of the French and English Tongues (1611). But I found no entry for flay. It should be here, but isn't.
My questions are the following:
Q1. Where did the meaning of to flay the fox as "to vomit" come from? It likely has to do with peeling the fur off of foxes, but is this really gruesome enough to warrant an idiom about vomiting?
Q2. What justifies the variant flea the fox? Is flea perhaps derived from a pronunciation of flay?
Q3. How does one reconcile the surely correct "vomit" interpretation with the final perplexing quote from Rabelais (the full context of which can be found here)? [Feel free to ignore.]
Given the mystery surrounding there's more than one way to skin a cat, I'm pessimistic there will be a definite answer to the etymology question, but I'm interested to hear people's thoughts.