The coolant at Chernobyl did not catch on fire, as the coolant was steam. Rather, it was the graphite moderator that burned. In a thermal reactor, which includes almost all of the operating power reactors (there might be a couple of fast reactors out there), the moderator slows down the neutrons. While a uranium (or plutonium) atom fissions, the emitted neutrons are moving at extremely high speeds and must be slowed down if they are to cause additional fissions and sustain the chain reaction.
In pressurized water reactors (such as Three-Mile Island) and boiling water reactors (such as Fukashima), water acts as both the coolant and the moderator. In an RMBK reactor, such as Chernobyl, graphite is the moderator and steam is the coolant. Almost all of the operating power reactors in the world are either pressurized water reactors or boiling water reactors.
The report I read stated that the reactor at Chernobyl was graphite cooled.
So, it was the graphite that caught fire. The photos from that time are very graphic, showing flames leaping in the shattered reactor vessel.