First thing of emergency treatment is vital signs and airway--blood pressure, heart rate, respirations, and pulse oxygenation of the blood. Burning gasoline will produce volatile vapors which will also cause inhalation injury to the laryngeal and pulmonary mucosa. A pulse ox less than 85% will result in intubation; otherwise supplemental oxygenation with a mask is the norm.
It hurts like hell. Placement of an IV, probably a central line, would be one of the first orders of business with administration of about 10 milligrams of morphine IV. This is a lot of morphine (IV). Fluid loss can be a big deal for a serious burn. An IV might start at half normal saline with 20 milliequivalents per liter of potassium at 100 millilters an hour.
The patient will then likely head to the ICU where he'll get some combination of antibiotics (burns weren't my specialty). If you want to pick something, I'd say ampicillan and gentamycin, but you could Wikipedia "burns"and go with whatever they list, or you could just say, "give him something to cover the skin flora."
Cold packs will be used on the second-degree burns, and a plastic surgeon will be called potentially to debride the third-degree burns.
The patient will go to a burn unit, which is essentially a clean room, wrapped in light gauze and given a shit-ton of pain medication. In fiction, it might be better to give an impression this is a lot rather than just a number like "If I give you any more you'll overdose and die."
As recovery progresses, you can do something cool like use medical maggots to eat away the dead tissue. Systemic infections are the biggest problem, and the most likely cause of death, especially if the lung tissue was burned resulting in various forms of pneumonia.
