The thing with mythical Atlantis is, it is exactly that: mythical. According to Plato's description in Critias, Atlantis was not just an island - it was an empire spanning the western Mediterranean:

All these and their descendants for many generations were the inhabitants and rulers of divers islands in the open sea; and also, as has been already said, they held sway in our direction over the country within the Pillars as far as Egypt and Tyrrhenia.

(Using this translation.)

The "Pillars" are the 'Pillars of Hercules', rock formations which flank the Strait of Gibraltar - Gibraltar itself being one of the 'pillars'. "[W]ithin the Pillars" then means the Mediterranean. If it stretches from Gibraltar as far as Egypt and Tyrrhenia (Italy), it covered quite a large area, covering more ground than for example the Carthaginian empire. We have no evidence for such a large empire having existed there at that time. Furthermore, we have no mention of Atlantis by ancient historians such as Herodotus.

Instead of something historical, Plato's Atlantis is a description of an ideal state, something to strive for. It is comparable to Thomas More's Utopia - nobody is suggesting Utopia was a real island some time long ago.

Atlantis is used by Plato to tell a moral story: people should be virtuous, or bad things will come to them. This is evident in this part of Critias (emphasis mine):

For many generations, as long as the divine nature lasted in them, they were obedient to the laws, and well-affectioned towards the god, whose seed they were; for they possessed true and in every way great spirits, uniting gentleness with wisdom in the various chances of life, and in their intercourse with one another. They despised everything but virtue, caring little for their present state of life, and thinking lightly of the possession of gold and other property, which seemed only a burden to them; neither were they intoxicated by luxury; nor did wealth deprive them of their self-control; but they were sober, and saw clearly that all these goods are increased by virtue and friendship with one another, whereas by too great regard and respect for them, they are lost and friendship with them.

If there is too much focus on worldly matters, then virtue and friendship are lost. Of course, this is exactly what happened to the Atlanteans (emphasis mine):

By such reflections and by the continuance in them of a divine nature, the qualities which we have described grew and increased among them; but when the divine portion began to fade away, and became diluted too often and too much with the mortal admixture, and the human nature got the upper hand, they then, being unable to bear their fortune, behaved unseemly, and to him who had an eye to see grew visibly debased, for they were losing the fairest of their precious gifts; but to those who had no eye to see the true happiness, they appeared glorious and blessed at the very time when they were full of avarice and unrighteous power.

Atlantis was not used by Plato only to describe an ideal state. In another of his works, Timaeus, we find the famous sinking of Atlantis. But Atlantis did not sink until after the Athenians had fought off the Atlanteans. As said above, mythical Atlantis ruled the western Mediterranean and was expanding east. In this way, Atlantis came into direct conflict with Athens:

and then, Solon, your country [Athens] shone forth, in the excellence of her virtue and strength, among all mankind. She was pre-eminent in courage and military skill, and was the leader of the Hellenes. And when the rest fell off from her, being compelled to stand alone, after having undergone the very extremity of danger, she defeated and triumphed over the invaders, and preserved from slavery those who were not yet subjugated, and generously liberated all the rest of us who dwell within the pillars.

Athens defeated Atlantis and apparently single-handedly destroyed its empire. Again, we see virtue playing an important role here. It was the 'excellence of her virtue and strength' which brought victory.

So both times Plato mentions Atlantis it is to emphasise virtue. There is no suggestion at all that all this has really happened. It is an allegory, a tale to educate people on what moral qualities are important.

Back to the article your question is about: it is grasping at all kinds of straws to construct a story. It is trying to connect all kinds of different events into a single narrative. I'm no expert on some of the things which are mentioned, but if you do find someone who has all the details I have no doubt they'll tell you it's misinterpreted, misconstrued, or just plain false. I'm not going to spend time research the details myself to relate findings here - having established that Atlantis was just an allegory, all other arguments in the article are irrelevant and must be wrong in one way or another.

Was the 'leak' of Lake Agassiz actually responsible for the Flood, and would that incident (if it happened as such) be responsible for submerging an Atlantis-like island?

This would be better for /r/AskScience, but simply put it's ludicrous. A freshwater lake, even one as large as Lake Agassiz at it's peak, has a miniscule amount of water compared to the ocean. Draining the entire lake would raise sea levels centimeters, nothing approaching the 200+ meters needed to flood that supposed island.

It's irrelevant anyways as glacial lakes don't really drain that way. Yes, there is a flood when one breaks through and starts to drain, however really on a tiny bit of the water drains at first, enough to flood and destroy a valley for a few hours maybe. The rest will drain slowly over the next hundred to thousands of years as the force of the water slowly carves it's way out to sea. Lake Agassiz likely drained in a whole series of these breakthrough floods over several thousand years, rather than over a Niagara Falls though, due to shifting glaciation continually blocking its previous exit. You can even see a similar phenomenon at Niagara Falls and can see it's in no danger of draining the Great Lakes into the ocean anytime soon.

Just wrote a 12 page paper on the origins of Atlantis. Essentially, Plato is recounting a conversation between three people (who likely never met, besides, Plato would have been 8 at the time) and the one person who talks about Atlantis explains that he was told the story by his father who heard his grandfather tell the story at a Greek version of an April Fools festival and the grandfather says he heard the story from a merchant who heard it from some Egyptian priests who said it happened a long time ago.

And that's it. That's the origin of Atlantis. Sure the guy explains this wonderful city that ruled the world but was defeated by the Greeks, but Atlantis was just simply a character to prove a point about a virtuous Greece.

The Atlantis we know today is a result of pseudoscience and Hollywood holding hands and skipping around... Which sucks because I really wish such a place existed. The closest thing to Atlantis would have been the island of Thera and the Minoans. Check it out!

The following things are facts:

• Sea levels in historical times are higher than they were during the last ice age, so coast lines were different, some islands were larger and many areas that were likely inhabited by ice aged humans are now submerged.

• Tsunamis, flash floods, river floods and even the occasional breach floods were things that actually happened, and probably affected prehistoric and ancient peoples at many points throughout prehistory. There were probably dozens if not hundreds of such events that at one point or another seemed like "end of the world" scale events to the people who were there at the time. There is no reason to relate ubiquitous flood myths to any one event since floods and other flood like events have always been fairly common the world over.

• There are cities and peoples, and even possibly civilizations or empires of which we know almost nothing today, and our knowledge of prehistory is spotty at best.

Given those facts, it's REALLY easy to cherry pick historical details here and there, suggest they're connected, and that they point to your favorite myth being real. But Atlantis isn't real. Consider:

• The story itself was made up to make a political point.

• The tropes he drew upon were common mythical fodder.

• He was trying to make an argument about whether or not Athens should become a naval power, so his allegory involved an island nation that became a naval power. (Had the debate been about silver mining, people today would be arguing about the existence of a mythical mountain kingdom.)

Ask yourself what's more likely, Plato needed to make a political point, and drew upon a historical example that perfectly fit his argument, and that the details and knowledge of that historical example had been preserved for over 7000 years, but were not ever once recorded anywhere else as far as we know. Or, he made up an example, and now modern "Atlantis hunters" cherry pick unrelated historical and archaeological details to try to suggest that Atlantis was real.