cobble isn't flammable. The wood was probably to close. Its can catch fire but it doesn't burn. The flame usually goes out after a few seconds.

Does Stone burn in Minecraft?

In Minecraft, fire will burn and spread until it has consumed the flammable blocks around it. ... Remember that stone does not burn! So to be safe, build the floor and walls around the fireplace out of some type of stone (even on the outside of your house).

What blocks in Minecraft keep burning?

Light a block of netherrack on fire, and it'll burn forever. Netherrack was added to the Java edition of Minecraft in Alpha version 1.2.