I don't believe Riot ever told us exactly how Veigar escaped captivity - only that he did so.
He is, however, one of the only Yordles not hated by a certain champion who specializes in making deals to transport people places, only to leave them miserable wretches in the end. Indeed, the wiki even lists them as allies at the moment.
Guess Noxian prison cells are a river too, huh?
As a child, Veigar was a normal yordle with one small exception - he had a deep curiosity for the world beyond Bandle City. The young yordle spent much of his time studying the rest of Valoran, and he jumped at the chance to join a business that traded with other major city-states. Unfortunately for both him and the world, a deal with Noxian trader turned into shady business and went bad; Veigar and his companions were subsequently set up to take the fall.
What if the deal was helping Veigar journey the world and the price was his freedom; a deliciously ironic twist. Tahm finds suffering delectable, and by having Veigar imprisoned for years, the River King had a steady stream of anguish flowing from Veigar's lonely cell.
Is good to see that I'm not the only one who thought the same.
Even if 
Veigar is not friend or enemy of Tahm, he IS a yordle... and Riot confirmed that the Demonfish knows all the yordles, including the Master of Evil.
I guess that is a Demon that is very interested in corrupting the hearts of people (after eating all the important things (and people) that are important for the person that made the "pact" with him)... Humans are easily corrupted, even more the ones from places like Bilgewater, Noxus or Zaun... but yordles? They are usually a happy race that would never make pacts with the "demon", excluding and 
, who aren't enemies of .
Now, lets remember the Taunts of Kench... he has A LOT of taunts... but, he only taunts 4 yordles, even if he is enemy with almost all their race:
Amumu
(Enemy) "I say, you're as 'fun' as a leaky roof." An insult
(Ally) "Coveting friendship is barely an appetite - but one I do so sympathize with." He is offering his "help" in order to corrupt him even more... it makes sense considering that Ammumu, as i said before, is sad and can be "corrupted".
Gnar
(Enemy) "Your conversation makes as much sense as a fish in lingerie!" The insult
_ (Ally) "Time is just a river, boy, let me take you back where you belong."_ Another "offering"... Gnar is a child (4 years old without counting the ice) and can be manipulated with ease, aside from the fact that he has anger problems.
(Enemy) "The enormity of the hat doesn't hide the vacancy beneath it!" Straight insult, he not even bother to make an "offering". Lets consider that she is the only friend of Veigar, and a very happy yordle.
Teemo
_(Enemy) "You're as likable as a rat in a bridle shop." _ Other insult
(Ally) "Every heart has its own hunger. Tell me yours." This one is interesting... the demon is not "offering" anything, but he is interested in corrupting "Satan", after all, Teemo is a psycho under that yordle mask.
... So... It makes sense that already "helped" to escape from the prison... and maybe, he ate the masters of Veigar? idk
Then the real question is, what did he take from Veigar?
Or even better.... what does he plan to take?
Another theory (although yours is just the sweetest omg)-
What if really did escape out of sheer spite and anger. What if he got tired and pissed, unlocked his in-universe incredibly OP Q and busted himself out like we've always thought?
But then, he'd decided to put the _world _ on it's knees. Now, that is something likes. That's something he'd not only gently help with, but get a reward of his choosing for doing so.
I mean, after reading your awesome theory I can't shake off Veigar sitting in his cell, just hearing Tahm sweet-talk to him. Lamenting and laughing. Telling to get his revenge.
But at the same time, I've always thought that his taunt "Do you want to reach your potential? It's a journey I could provide." is for rather than for 
.
oooooo id believe it
Do you guys think Tahm is a darkin, he is listed as an ally of aatrox which i found to be very strange and rather random. But think about it what do the darkin do they interact with and "help" mortals in order to reach their own ends for tahm thats sating his hunger and for aatrox his lust for battle.
I've read that Veigar was free by Teemo but Veigar left Teemo for dead after he was free (whether or not this is canon or not I do not know).
That's... actually pretty interesting of a theory. Huh. Makes sense.
