Please, tell more, weight, length, etc.
I have been playing flax yarns. I have bought some well known Irish flax yarns, like Barbour's, Campbell and Patons. Every of these are quite good. Here is one example, Campbell 30/3 linen, 16 strands, 200 pounds, 165 cm (65"), tenacity 32,5 cN/tex, 83,7 grains without wax and center serving, 90,5 grains waxed and 96,5 grains waxed and with center serving. Servings are cotton. And this was old linen. With new and a bit better linen, about 75 grains string could be possible.
By the way, this is the best linen yarn I have now. My best silk thread (filament silk, not spun) has tenacity 41,20 cN/tex, so it is about 27 % stronger per mass than the Campbell linen yarn. Silk of course stretches but I don't think it is a problem, if the string is well prestretched.