How flammable is oak furniture?

Oak furniture's flammability is based on a number of factors, and could be hard to quantify in your context. Things such as curing time, moisture content, finishes and thickness are factors in the ability of anything to burn. With a volatile finish and relatively thin piece of furniture, it could burn very easily. A piece with a non-volatile finish, thick, with a high moisture content would take much longer to ignite.