1. To cause something to start burning: Janet used a match to conflagrate the charcoal in the barbecue outside on the patio in order to roast their meats.
2. To begin to burn or to burst into flames: The rags which were soaked with benzine quickly conflagrated when they were set on fire by the arsonist.

Go to this arsonist link so you can see this conflagrating entry in action.