Answer:
It depends, really. A rock's friability is the ability of a rock to easily be broken into smaller pieces(easy in the sense of hitting it with your hand).
Whether or not a rock can burn is based more off of a rock's composition. For example, coal will burn, quartz will not. Rocks made up of organic material(coal, peat, lignite, oil shale) will burn - hence, fuel.
A rock can, though, be organic and friable. So its possible to have a friable rock that can burn. But ignition isn't dependent upon friability.