The safest and surest method of stump removal is to call a professional tree-care company and have them "grind" the stump out. If that expense doesn’t appeal to you and you have the energy, you can dig down around the stump to unearth the roots and cut and remove each one as you find it. You will still need to take an axe and cut apart the stump to remove it.
Building a fire is not only unsafe, it is slow, and you run the risk of the fire smoldering underground in the roots, and surfacing in some unexpected place like the foundation of a building. Chemical stump removers are also slow (sometimes taking years). Using flammable liquids is not recommended.
