An incendiary device is a bomb. An incendiary statement is, "You're ugly and stupid." Both are likely to produce an explosion of one kind or another.
Incendiary means more than flammable. It means explosive, in both a literal and figurative way. If you're a radical who changes the world by exciting people and makes as many enemies as followers, you're an incendiary figure. The speeches you give that rile people up are incendiary. The fires you set are also incendiary, and by setting them you are also likely to be called an incendiary — someone who burns things, more commonly known as an arsonist.