It is illuminating (heh) to look at the full text:
Oil. Oil usually comes in a clay flask that holds 1 pint. As an action, you can splash the oil in this flask onto a creature within 5 feet of you or throw it up to 20 feet, shattering it on impact. Make a ranged attack against a target creature or object, treating the oil as an improvised weapon. On a hit, the target is covered in oil. If the target takes any fire damage before the oil dries (after 1 minute), the target takes an additional 5 fire damage from the burning oil. You can also pour a flask of oil on the ground to cover a 5-foot-square area, provided that the surface is level. If lit, the oil burns for 2 rounds and deals 5 fire damage to any creature that enters the area or ends its turn in the area. A creature can take this damage only once per turn.
Consider how you would rule for a creature covered in non-burning oil who entered a burning oil covered square. I would rule that they would take damage twice; you may rule otherwise.
Also a creature moving from burning oil covered square to oil covered square takes damage in each square but takes no more damage if they retrace their steps - this is clearly an abstraction - injury from heat in real life is a non-linear function of heat transfer, temperature and duration.
You can approach your ruling in several ways.
The RAW way
Note: this is very un-5e.
"You can also pour a flask of oil" so you can't pour 2 so the problem doesn't come up. Of course this does not prevent you from pouring oil on an adjacent 5-foot-square area.
The quasi-scientific way
1 pint (0.6l) of oil evenly spread across a 5-foot square (2.3m^2) is about 1/100 inch deep (0.25mm). This is considerably less than the meniscus you would expect on oil (~2-3mm) so it is more likely that the oil is concentrated in a puddle or series of puddles across the square; especially since you "pour" it.
On that basis, it would be reasonable to rule that it would cause additional damage up to the point where the whole square was covered to a depth of say 2mm (8 flasks) after which each additional 4 flasks would extend the duration by 1 round.
The magical way
"A burning flask of oil is the physical manifestation on the material plane of the ongoing struggle between the elemental forces of water (oil), fire, air and earth. This is why the same amount of oil will burn for twice as long when spread on the ground as it does when spread over a living creature for a living creature contains within it the essence of fire which the earth lacks" - Jongril the Sage, CY 456.
It works this way because it works this way, so there!