This theory comes from a comment I made on this post by /u/HubertFarnsworth95, who speculated on why FromSoftware included Earthen Peak in the final DLC. Rather than brush it off as a simple call-back, he brought up some interesting observations and ideas, and got me thinking about the nature of poison and toxin in Dark Souls. After some people showed interest, I decided to turn it into a more complete theory, and I'm hoping the community might expand on it further.
To summarize, it appears that in all three Dark Souls games, toxin is closely related to the Chaos Flame, most likely a side-effect of (or counter to) its creation. The evidence for this is actually pretty obvious, and I honestly feel dumb for not noticing it earlier.
I'll start with locations, which began this whole idea. In Dark Souls 1, we descend through Blighttown to reach the Demon Ruins. At its base is a massive poisonous swamp, filled with bugs and infected undead, and the domain of Quelaag, daughter of chaos. We find Quelana and the Fair Lady here as well. The refugees of Izalith have made Blighttown their home, and those who serve the Fair Lady are mutated from parasites, serving as hosts to her eggs. If you speak to her, she reveals the ones around her are still, and dead. They need a human host to survive, and those such as Eingyi willingly grow these eggs on their backs.
In Dark Souls 2, you pass through Harvest Valley and Earthen Peak, which have unleashed a poisonous gas from their excavations. Most enemies are hollows and skeletons, but we also fight desert pyromancers here as well. Beyond this, we find the Iron Keep, another kingdom sunken into lava and ruled by a demonic overseer. Its former ruler, the Iron King, created the Smelter Demon only to die by its hand. His corpse became the vessel for yet another demon, Ichorous Earth, which is the monster we fight as the Old Iron King.
Finally, we get to DS3's Earthen Peak. It suddenly makes sense that they would include this area, as the bosses are a pair of poisoned demons. They even vomit toxins on us during the battle. The description released with the preview photos explains it too: "With a grotesque look having been exposed to poison, their flame is fading away…"
The one deviation from this pattern is Farron swamp, which doesn't lead directly into a demonic area. Instead, it leads to the Catacombs of Carthus, which then transitions to Smouldering Lake and the Demon Ruins. As other commenters have pointed out, though, the catacombs are home to unique pyromancers, and there are a couple demons in proximity to these areas (Stray/Fire.)
Something I realized later, however, is that the Ghru are only present in both areas. The Ghru of Farron swamp have poisonous weapons and use deadly mists, but the "clerics" of the Demon Ruins wield advanced pyromancies and wear masks similar to Capra Demons/Aldia Warlocks. I'm not sure how the Ghru came to be in the Demon Ruins, if they were previous citizens who mutated or if they migrated from Farron. Either way, they are another connection between a poisonous swamp and the chaos flame.
After thinking about these locations, it suddenly hit me that Poison Mist and Toxic Mist are pyromancies (duh.) Both were created by Eingyi of the Great Swamp, though he was cast out as a heretic because of it. Item descriptions from DS1 and 2 suggest toxin is an unnatural derivative of pyromancy, and goes against its very concept.
Toxic Mist (DS1): "Why was Eingyi driven from the Great Swamp? One only need cast this pyromancy, a perverse diversion from the art of fire, to find out."
Poison Mist (DS2): "This spell contradicts the very principles of pyromancy, suggesting that its creator had a heretical streak."
However, in DS3, things take an unexpected turn…
Poison Mist (DS3): "Eingyi was driven from the Great Swamp, however his pyromancy continues to succeed him. Perhaps dwellers of the Great Swamp were reminded that their very existence is one rooted in heresy."
Toxic Mist (DS3): "Driven from the Great Swamp, they say that at the end of his journey, Eingyi happened upon a virulent poison and a young lady."
These descriptions strongly suggests that, although Eingyi discovered the applications of poison, it was already an inherent part of chaos. I always assumed he was responsible for Blighttown's condition, but since Quelaag's Domain was apparently the end of his journey, the poison must have already existed there for him to discover it. Also, it may be "virulent" because of its proximity to Izalith and the Fair Lady, a demon who feeds off humanity. Keep that in mind for later.
"And with Fire came Disparity…"
Here comes the speculation. I think the safest assumption is that poison/toxin is the disparity of chaos, just as dark is to light, cold to heat, life to death, and so on. Few things in Dark Souls exist without some form of antithesis, and the Chaos Flame should be no different.
The recurring theme in all these areas is that flame is tempting, seductive, but also deadly. Fire can be gorgeous and powerful, but it can slowly consume your soul as well. We see visual representations of this seductive nature in Quelaag, the desert pyromancers, and Mytha. All of them appear provocative yet monstrous, and lure unsuspecting victims into their domains. Many believe Quelaag used the bell to farm humanity for her sister based on the Fair Lady's dialogue, which suggests Quelaag aided and visited her frequently. Desert pyromancyers use their looks to seduce their opponents, while their queen Mytha used poison to beckon lost souls to her land and turn them into manikins. She was corrupted and disfigured by desire for the Iron King (arguably,) and even the game questions if the poison caused her passion, or if her passion caused the poison.
With this theme of poisonous seduction in mind, the connections between chaos and poison makes a lot more sense. Here is a lengthy list of choice descriptions to support this:
Power Within (DS1): "Excessive power eats away the life-force of its caster…"
Chaos Storm (DS2): "Those who sought great power were consumed by their own desires."
Immolation (DS2): "If a person is truly desirous of something, perhaps being set on fire does not seem so bad."
Rapport (DS3): "The living are lured by flame, and this tendency is elemental to the art of pyromancy."
Flame Fan (DS3): "Zoey possessed true beauty, as did all the desert pyromancers, but hers did not poison…"
Edit: I forgot to mention my last conclusion. The chaos flame created demons, but it also created various parasites and insects as well. We can see this in chaos bugs, sunlight maggots, vile maggots, and even the Centipede Demon. Don't forget, the two daughters of chaos are part-arachnid as well. Many of these parasites infect and mutate humans/undead, turning them into greater abominations. When this happens, I think the clash of chaos and humanity creates these poisonous environments.
When Izalith fell, the daughters of chaos fled to Blighttown and began building their nests. From what I can tell of Eingyi, they birth parasites from their eggs. These creatures are like lesser demons that feed off humanity, and may be the cause of Blighttown's corruption. We find plenty of insects here, such as the mosquitos and leeches, both of which feed off human blood (the blood of the Dark Soul!) There is also the wall parasite guarding a pyromancy, and the Cragspiders, which many theorize to be mutated hollows. I'm certain that the design choice of the chaos daughters and the mutations of the Blighttown residents are no coincidence. When the flames of chaos meet the darkness of humanity, the results are poisonous.
If all this still hasn't convinced you, here's my last piece of undeniable proof: You can trade a dung pie to Snuggly for demon titanite. Case closed.