Isaac shoots grey tears that leave a puddle of grey oil creep when landing, which will slow enemies that are standing in it. If Isaac walks over an oil puddle, it will ignite it and produce a flame that can ignite and spread to other oil puddles in close proximity.
Oil flames will shrink when dealing damage to enemies, with variable damage per tick based on the flame's size — A single flame will deal damage a maximum of 4 times for upwards of 60.5 damage in total.
The oil creep puddles and the flames both have a duration of approximately 5 seconds.
Notes
Size of the oil puddles, as well as the flames from igniting the oil does not scale with Isaac's tear size or any of his other stats.
The burn duration of the flames is separate from the oil creep's duration, meaning the flames can still be burning even when the oil creep that it has ignited from disappears.
Fire produced by the oil creep have similar behavior to the flames produced by Red Candle, including the flames' ability to block enemy projectiles.
The oil puddles act similarly to the gunpowder creep created by various Burning Basement enemies in Fiend Folio, except the fire it creates will not hurt Isaac. As such, anything that can ignite gunpowder will also ignite oil.
Interactions
Aquarius: Changes the color of the creep trail, but will not be able to be ignited.
Brimstone / Technology: Lasers will produce oil puddles under enemies they hit.
Abyss: Absorbing Modern Ouroboros spawns a brown Abyss Locust that produces oil puddles on hitting an enemy and immediately ignites them.
Lost Cork: Increases the size of the oil puddles. Does not affect the size of the fire created when igniting the oil.
Video Showcase
Trivia
Modern Ouroboros was unused in the initial The Binding of Isaac: Afterbirth+ release of the Fiend Folio MOD.
Modern Ouroboros is a reference to the LISA fan-made game LISA: The Pointless, and the boss Anaconda Virtue. The name of the item is based on Anaconda Virtue's theme song, Modern Day Ouroboros.
Red Candle, including the flames' ability to block enemy projectiles.
Aquarius: Changes the color of the creep trail, but will not be able to be ignited.
Brimstone / 
Technology: Lasers will produce oil puddles under enemies they hit.
Fire Mind: Flames produced by these items can ignite the oil.
The Candle: Will not ignite oil creep.
Abyss: Absorbing Modern Ouroboros spawns a brown Abyss Locust that produces oil puddles on hitting an enemy and immediately ignites them.
Lost Cork: Increases the size of the oil puddles. Does not affect the size of the fire created when igniting the oil.
