Swim underwater. Try to avoid the burning oil as much as possible. Since it can only burn on the surface, and that will likely be engulfed in flames, stay below and swim as far as you can below the surface.
Swim for short intervals. Don't try to hold your breath too long or the overwhelming urge to breathe will have make you panic and come up too fast and get burned.
Look up and stop swimming. You will be able to see the fire on the surface. If you can't see any flames, assume they are there anyway.
Splash the surface while still underwater. Splashing will throw the burning oil and clear you a small area. You should be able to see a hole in the surrounding flames.
Come up and breathe. Close your eyes to protect them. Use your hands to surface and come up vertically. It's going to be hot. Keep your eyes closed, turn your head to the side, staying low in the water and take a quick breath. One breath out, one in.
Dive feet first and resume swimming under the surface until it's time to take another breath. If you keep a cool head, you can make indefinite progress until you make it out of the burning oil field safely.
Splash continuously if you are in a situation where you can't swim underwater. Make progress through the water and out of the burning oil by splashing the oil away constantly. Front, back and sides. To do this and make any progress, go from a low breaststroke to a backstroke and back again, turning constantly and moving forward. This can be done with one hand while the other stays in front of your face to shield it.
