Flemish string ok?
A true Flemish string isn't suitable for linen, but the modern definition is, just to be really confusing!
"Real" Flemish strings are made with full length fibres glued or "gummed" and slightly twisted, with a laid-in top loop and a reverse-twisted bottom section, which is then used for a bowyer's knot. This is perfectly fine for strings made of full-length hemp fibres, as they can be grown and cut longer than a bow. Flax however, doesn't grow long enough so needs to be made into a reverse-twisted string.
Your best bet with linen is actually to make a three-ply fully reverse-twisted string instead of pretending it's FastFlight etc and just making up a normal string. Bundle up three groups of odd-numbers, twist them all one way then twist all three into a string in the other direction. This way you get the benefit of spreading all the short fibre weakness into a far stronger string, plus that extra thickness in the loop.
This has worked for me for bows over 130lb, whereas other string types consistently fail.