To get a concrete feeling of how much flammable cellulose nitrate is, buy a set of ping-pong balls and set them alight. The speed of combustion is unexpected, definitely faster than common polymers.
The explosive uses a different proportion of nitrate than the polymer, and yes, it can detonate, or it can burn, including without air. Still in use as a smokeless military rocket propellant, as a colloid in nitroglycerine. The not so funny part of it is that nitroglycerine may separate from nitrocellulose on prolonged storage.
Items made of cellulose nitrate will probably rise false alarms by explosive detectors, at airports for instance. Not convenient. Cellulose acetate should avoid this difficulty.