It is a chemical property because combustion is a chemical change, and how easily something will burn or ignite, is a chemical property.
A chemical property changes the substance chemically. That means that the bonds will either break or new bonds will form. If you flame a tissue, you will see that it cant be changed to a tissue anymore, it will be burnt. That is because it is flammable and a chemical change happened. Which means that bonds broke or formed to make the new substance.