Wool is difficult to burn, even though it is flammable. It generally doesn't burn hot enough to keep the reaction going (it is not a sustained chain reaction).
Cotton however, which is actually the fabric made from plants, is very flammable and burns quickly. Silk burns even faster than cotton. This is because they are mostly made of hydrocarbons, which have a lot more "potential" energy stored in their chemical "bonds".
I confirmed most of this information at
phoenix.gov, but since I was using Yahoo as search you might find some different organization talking about it in the first few entries of your search results.
I always thought that it was stupid to get wool from a plant. It should be changed to cotton, and an alias made to convert all of the dumb wool blocks to cotton. Then it would make sense for it to be made a furnace fuel, since it is flammable, but it shouldn't last long.