First, tell me, how does a person that has no desire to be baptized, no desire to be a Catholic, no belief in Christ or the Holy Trinity (like a Jєω, Hindu, Buddhist....), how can he be saved by this quote from Trent?  

Or are you just talking about a catechumen that is on his way to be baptized and gets hit by lightning and dies instantly?

No question about it, obviously the person must have the desire to be baptized. That is taken for granted when anyone is baptized.  

However, the latin "Baptismus flaminis" sense is that of inspirational (inspired by a flame, i.e. Holy Ghost)

But we're talking about Trent, not the opinions of saints.  When Trent used "desire" the latin word is "votum" which means "a vow" not simply to be "willing".  In other words, according to Trent, in order to be justified, the person has to "vow" to be baptized, or make some similar solemn promise.
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Obviously, a catechumen would be the only type of person who would be in the position of 1) knowing about baptism completely, and 2) being able to promise God that he'd become a member of the Church.  All others, could not fulfill or even make such a solemn promise.

Don’t derail my thread. I made it specifically to discuss this with Lad.

Sounds like you are a typical denier of EENS hiding behind "implicit" and that I hit the nail on the head with my questions. 

Lad, I’d like to discuss our disagreements one issue at a time.

I first heard the “and not or” argument many years ago when the Dimond brothers made it. I’m not sure if you got it from them or they from you. Anyhow, My problem with this argument is this:
      A) This argument is of recent origin. No pre VII Catholic theologian, that I’m aware of, has ever made this this claim about the word used being “and” not “or”.
      B) All theologians prior to VII interpret Chapter VI of Trent as proof of the Church’s teaching on baptism of desire, thus the word “or” is essential to it’s interpretation.
      C) Can you cite a theologian that agrees with you on this? As you know, Father Feeney, who wasn’t a theologian, never believed this.
      D) You gave this analogy: “I cannot play a game of baseball without a bat or a ball.  Does this mean that I CAN play baseball if I have ONE or the OTHER?” Sure you can play baseball with one or the other since you didn’t exclude the possibility that you may already have one of the other items.

Let’s turn it around: I can play a game of baseball with a bat or a ball. Now, does this mean that I CAN play baseball if I have ONE or the OTHER? Sure you can, provided you have the other item also.

The point I’m making is that the double negative used by Trent essentially says the same thing, except it seems a bit more exclusive which is probably why they used it.

No, I came up with this reading of Trent on my own long before the Dimonds said the same thing.  I initially believed in Baptism of Desire simply because I thought that Trent taught it.  So one day I happened to be reading Trent's entire treatise on justification in Latin.  What I found was that this particular quotation had been lifted out of its entire context.  If you read the entire thing, a picture emerges.  What Trent is teaching, against the prevalent Protestant errors, is in fact the necessity of cooperation between grace and free will.  Grace is given freely, but then the WILL must must cooperate.  So the ENTIRE POINT of the Treatise is that BOTH grace ex opere operato AND the cooperation of the WILL are necessary.  So it would seem strange then for Trent to be teaching the whole time that both grace and will are necessary, and then suddenly to switch gears and say ... but grace OR free will are necessary for justification.  There's even a Canon in Trent which condemns the proposition that one is justified by Baptism even without the intention/desire to receive the Sacrament.

Now, the word commonly translated as "desire" is actually the Latin votum, which is a noun form of the Latin verb that means "to will".  Desire is a watered down translation made, IMO deliberately, to weaken its force.  It's more like a "vow" (our word "vow" also comes from the same Latin root).  Let me give an example.  I can DESIRE all I want to get married, but that does not mean I am married.  I can get engaged, set a date, rent out the reception hall, hire a photographer, have every intention and desire to get married, but then bail out five minutes before pronouncing my "vows" ... and I am not and never was married.  There must be some FORMALIZATION of this intention.  Now, one could argue that a catechumen could be close to having this kind of will/intention/vow to get baptized.  So in order to make BoD apply to all manner of infidels, the force of it had to be weakened.  Even St. Robert Bellarmine explicitly limited BoD to the catechumen.

In any case, on its face, the expression, "I cannot play baseball without a bat or a ball," is ambiguous.  You COULD take it that I cannot play baseball without having EITHER a bat OR a ball.  Or you could take it as meaning that I cannot play if EITHER is MISSING.  So on the surface, you could take it the BoD way, or else you could take it the way I read it.  But if you take the VERY NEXT SENTENCE of Trent, this sentence is immediately disambiguated ... in favor of MY reading of it.

To paraphrase, justification cannot happen without the laver or the desire, for Jesus taught that, in order to be born again, one must be born of water AND the Holy Spirit.  This is clearly making the following analogy (if you recall analogy format from the SAT) --

laver:desire::water:Holy Spirit (laver is to desire what water is to the Holy Spirit).  

Trent deliberately uses the descriptive term "laver" instead of, say, the Sacrament, precisely to drive home the analogy with this teaching and Our Lord's "water AND the Holy Spirit".  See, again, if you read the entire context, Trent had just spent several paragraphs explaining how it is the Holy Spirt who INSPIRES this cooperation of the will.

So to take this passage the BoD way would be to say:  I can play baseball with either a bat or a ball, since the coach said that I must have a bat AND a ball to play baseball.  It's ridiculous on the face of it.

Water AND the Holy Spirit immediately disambiguates the "not without the laver or the will for it" into my reading of it, and not the BoD meaning.

I stand by this reading of Trent as absolutely the only one that makes sense.  As for why other theologians didn't read it this way.  Well, St. Alphonsus actually cites teaching on the intention to receive CONFESSION (combined with perfect contrition) as sufficing to RESTORE someone to justification after it has been lost through sin.  But if you look at the passage on confession, Trent explicitly states, "EITHER ... OR".  If Trent were teaching the same thing here, you would have expected the exact same unambiguous phraseology, "EITHER the laver OR ELSE the desire".  But it's not there in the passage regarding Baptism.  In theology manuals AFTER the Council of Trent that were used in seminaries, BoD was still presented as a disputed question, with BoD referred to as the "Augustinian" position (by contrast with other Fathers who rejected it).  So in the immediate aftermath of Trent, this passage was NOT in fact read as closing the debate on BoD.  One or another theologian first read this as promoting/endorsing Baptism of Desire ... and then everyone else simply followed along and made that assumption without re-examining that interpretation.

So, if someone could persuade me that the sentence, "I cannot play baseball without a bat or a ball, since the coach said that I have to have a bat and a ball to play baseball," actually means that I can play baseball with EITHER a bat OR a ball, then you could convince me that Trent teaches BoD in this passage.

Canon IV after the Treatise on Justification:

CANON IV.-If any one saith, that man's free will moved and excited by God, by assenting to God exciting and calling, nowise co-operates towards disposing and preparing itself for obtaining the grace of Justification; that it cannot refuse its consent, if it would, but that, as something inanimate, it does nothing whatever and is merely passive; let him be anathema.

This is why Trent explicitly taught that the votum (=will) is required.

Think about this.  If Trent had in fact been teaching that EITHER the Sacrament OR the desire suffices for justification, then Trent would be contradicting THIS VERY CANON.  Trent would in fact be saying that Baptism could justify WITHOUT the intention/will to receive it.  But this would be absurd.

That "Baptism or the will"  ABSOLUTELY CANNOT BE an "either ... or" proposition.  BOTH are in fact required.  If the BoD interpretation has it that the VOTUM can justify without the Sacrament, then it's also the case the Trent is teaching that the Sacrament can justify without the will or desire to receive it ... which Trent itself anathematized.  So in a sense, TRENT ITSELF anathematized the BoD interpretation of this passage.