Immediately before Dante and Vergil reach the City of Dis, they ride on the boat of the sinner Phlegyas. He's in Hell for setting aflame a temple of Apollo (Phlegyas's wife was a lover of Apollo, she cheated on Apollo, and Apollo killed her). Later, we see those sinners who are violent toward other people burning in the river Phlegethon. Dante describes the river as flowing with boiling blood (quite fitting for the contrapasso of these sinners). Plato described it as a river of fire, and the name translates to "flaming."
What Phlegyas and Phlegethon have in common is their common prefix, the Greek root relating to fire. Phlegyas's fire was his internal rage, while Phlegethon's fire stems from the hate of the sinners it houses.
Later, Johann Joachim Becher postulated that fire burns because of the presence of a molecule called phlogiston. Without this new molecule, a fire wouldn't burn. Turns out, this molecule was oxygen, and Becher's theory, while a decent hypothesis and important scientific step-stool, was proved obsolete. Phlogiston also shares the same prefix for fire.
Here's a funny picture of Becher for your amusement: