Linen cloth and raw strands of flax are two different critters. Linen cloth will help keep splinters from rising, as does burlap, silk, etc. It does not improve bow draw weight or cast.
Raw combed flax a.k.a Flax Strick is combed long fibers. Available online from The Woolery and similar weaving suppliers. You pre-wet the "hank" with water, wring it out, then soak it in slightly thinned TBII, TBIII, or Hide glue and applied in the same manner as sinew. Flax is much less smelly to work with than sinew but works nearly as well. Don't use it on strongly reflexed bows though as flax does not stretch as well as sinew.