flax is a natural fiber basically more common in the old world than here in the USA
Here Cotton is prevalent and linen is made from cotton, clear back to the Egyptian days.
linen also comes in different thicknesses.
cotton,linen, denim etc is measured by weight.
they increase the weight two ways. using a thicker diameter thread, or weaving it titghter with more threads per inch.
Try your bed sheets ( all cotton ones) they make good patches
very lightweight blue jeans (like for toddlers) will also work