This move is called "Sto'n'go". After villain already put 1/3 of his chips in the pot, he will never fold to a shove, getting 2:1 odds. So, it's possbile to call him and jam on the flop. For example, on this flop villain will have tough decision, if he holds a pocket pair 22-TT. Sometimes villain, who holds like AQ-AK, will fold to jam on low-connected flop, like 578.
Stop'n'Go is effective, when you hold a hand, strong enough to shove, but suppose opponent will never fold and you probably will play coinflip (like small pocket pair), and stack sizes are shallow (6-7BB). Preflop you have no fold equity, but on the flop, where you are first to act, you could get it.  
Main idea of Stop'n'Go is to force villain to FOLD, not to call, as I undestand.

 WBR is right.  The idea was, my hand is strong enough to put my stack in with preflop.  However, given virtually any flop and any hand villain has, he will be making a mistake if he folds given that i'm going to jam my entire range on the flop (this is even if he has a hand like 9T and the flop is AKQ).  Since villain will never fold PF, why not give him the chance to make a mistake and fold on the flop sometimes.

He's getting about 2 to 1 on his money, and he's 18-27 % to win with unconnected undercards against your K-high on the flop, so can't really see how you concluded with "virtually any flop and any hand villain has, he will be making a mistake if he folds". Actually, his optimal play against your play is to always call with K-high (6 kicker) or better on any flop, and given the villain I think this is close to his calling range, so you pretty much picked the worst possible time and hand for a Stop 'n Go.
In your example, T9 on AKQ board, he's 18 % to win and a fold is very much his best option.

 Consider the other hands in my range.  You could poker stove this I'm sure.  Take any hand that the equilibrium says I should call with 6BB, so include 98o, T6s, and all of that fun stuff.  Then weight T9's equity against that range and find out if it is greater than 33% or w/e it would need to call the flop jam.  It might be less, it might be more.  I honestly have no idea.
You might be right that this might be one of the worst boards for my hand/play.  I'm not sure that any line other than jamming the flop is good though (you'd rather c/c or c/f?) given that we take our line preflop, and I think our line preflop is perfectly acceptable and likely optimal vs. the majority of players.
I don't know what it means to pick a bad time or bad hand.  Is that just because the flop ran out bad?

First off, I took no consideration to the flop (AQJ) whatsoever, everything I wrote was considering a random flop/a random flop where you missed.
Secondly, if you consider the pre-flop odds he is of course correct to call with any two cards when you jam over his raise, no question.
However, you didn't jam preflop, you're jamming your entire range on the flop, and it seems your opinion is (and for the arguments sake let's say it's entirely true) if he had known this information he would also be correct calling any two cards after the flop, but he doesn't and thereby folds more hands than he should and therefore the Stop 'n Go is +EV. What you seem to be missing is that doing the Stop 'n Go with K5o, the times you will "force out a hand that should have called given your range" he's a great majority of the time correctly folding a hand worse than yours. So with 98o, T6s etc I think a Stop 'n Go is the best move, but with K-high YOU are making his original mistakes a good play.
My conclusion: Stop 'n Go in general = good, Stop 'n Go with K5o = bad.
If you do call preflop, jamming the flop is of course the best line, but can't think of any player where jamming preflop is less EV than jamming flop given the hand (K-high) and the stacks in this particular hand.

Does tournament life factor in here at all?
With the stop n' go, we will have 60-75% fold equity on many flops (depending on the villain's pf range and tendencies and the flop texture), meaning we get to see another hand with 200 more chips 60-75% of the time.  Also, some portion (is it safe to assume 25%?) of 25-40% where we are called, our K5o will win, adding another 5-10% chance of seeing another hand.  So this play has as much as 70% chance of letting us see more cards, with 200 or more additional chips in our stack.
With the preflop shove, assuming we have 48% equity vs his range (I don't know the villain's tendencies in this particular example, but K5o has 48% equity vs the top 65% of hands preflop) then we have maybe a 48% chance of seeing another hand but instead with 600 more chips.
 
*edit* Is it a waste of hand value?  K5o is strong but it isn't a fantastic hand.  It doesn't dominate many hands in his range (Q5? J5? K2?) but is definitely dominated quite often (A6+,K6+, etc).  And sure, we let villain fold sometimes where a preflop shove would net us more chips, but instead we have a higher chance of seeing more cards, and getting the button.
*double edit* thanks for this thread on both sides of the discussion, it really made me think about the merits of each play.  I haven't actually tried the stop n' go yet but hopefully I can find a place to work it into my game... coaches, if you care to give away this info, how often do you guys (recommend to) use this play?  Is the play still viable if the postflop shove is as much as a 1.5x overbet?  Any other considerations on villain type, etc?

Solid points.  The only issue that would exist on theoretical level with what you said is that by removing certain hands from our Stop n Go range, we weight our distribution unequally and thus villain (theoretically) could come up with a plan better than just never folding postflop (say, never folding on kings or aces, but folding some % on jacks).  Of course, this will never, ever, come up in real-time play, so you can absolutely never Stop n Go with K5o and never be exploited for it.
I think we're having a discussion along the same lines as the unexploitable strategy vs. unexploitable play arguments.  Jamming 64s at 14BB is a +EV play if you are playing jam/fold and it is part of an unexploitable strategy.  However, if you take that hand in isolation, of course it looks ridiculous and it's easy to come up with a calling range that destroys it.
EDIT:  Yea, more on the strategy thing... It's like, this is a mistake a lot of players make in the end game.  They minraise all of their really strong hands at 10-15BB and jam their air, because they see "oh, i can jam 86s here, I'm going to".  Then when they have AA, they're like "well, it's MORE +EV if i minraise or limp instead".  What they don't realize is that if they don't jam AA and other strong hands, then jamming 86s is no longer profitable.  And they get all upset when I call with K6s for 14BB!

I regret editing out the part saying this is of course level 0 thinking... I absolutely agree with you on the strategy part, and would like to add that the play (Stop 'n Go lower end of range only) is far less exploitable than it is predictable. Actually the Stop 'n Go in general is very predictable as you want them to fold some hands when in fact they would be correct calling with ATC. If you fear someone decides to get cute and fold some marginal boards where you're more likely to have connected (e.g JTx boards), you could expand your range a tiny bit downwards to make up for the lost EV. Doing the same play with the higher end of the range still seems spewy (microscopically, but still.)
Btw, added a note on you on stars; min-raise junk and jam monsters during 50/100... :D
PS: I would really enjoy reading an article where you explain "unexploitable play vs unexploitable strategy" in more detail and depth, and perhaps explaining the metagame in general.
Thank you for taking the time to explain your actions and discussing this, it feels like a free semi-coaching lesson.