I've used raw, combed flax for a bow backing. It's like sinew in many respect, except it doesn't dry into a considerable reflex. I think it's superior to sinew because it's lighter, less prone to moisture absorption, and much easier and quicker to apply. I've actually grown some flax for backing and strings, but it's long process to get it into a workable state.
By the way, linen is the spun and woven form of flax, just as canvas is to cotton.