In Dungeon World, "damage over time" is not a mechanic; this is a purely fictional construction. If you're on fire, the fictional consequence is that you're on fire! This creates conditions for various GM moves that follow from the fiction. As long as the underlying fictional state isn't dealt with (you're still on fire!), conditions remain ripe for consequences, as expressed in the GM moves you make.
For an NPC that's on fire:
You can reveal an unwelcome truth that their screaming and flailing has attracted the attention of something, which you can hear quickly approaching from around the corner. Note here that we're not so worried about the mechanics of killing the NPC (the NPC can just die when it's appropriate), but rather using the situation to think dangerous and fill the character's lives with adventure.
You can put someone in a spot by having the flaming NPC charge at one of the PCs. If they get a partial on a Defy Danger dealing with it, this could segue into separate them (Cleric, the scattered flaming oil has created a wall of flame between you and the party) or maybe use up their resources (Thief, you narrowly dodge out of the way, but one of your packages of poultices and herbs attached to your belt is aflame; what do you do?)
Give an opportunity that fits a class' abilities: "Jimmy the orc has finally stopped moving, but the corpse is still aflame. The distant growls are swiftly approaching. [Salamander] Immolator, what do you do?"
Offer an opportunity, with or without cost: "The enemy magus is rather distracted by being on fire and has stopped casting his spell. Fighter, you see an opportunity to engage; what do you do?"
For a PC that's on fire:
Deal damage: "You continue to burn, take another 1d6 damage." or "Your skin has started to bubble and melt a bit; take the scarred debility."
Tell them the requirements or consequences and ask: "Sure, you can charge that shaman, but you'll have to run past the Fighter to do it and you'll need to Defy Danger to avoid setting him alight as the sticky flame scatters from your body."
In general, I'd consider continuing to be on fire to be a fictional condition that offers repeated golden opportunities to make moves, likely harder moves than you'd normally make without a miss involved. So in Dungeon World, it's really more "danger over time", in that not dealing with an ongoing persistent dangerous fictional condition will create serious ongoing complications. Other examples include things like poison gas filling the room, being out in the open and under fire from a large group of archers, having a larval demonic abomination growing inside your brain, etc.