I tend to qualify the word linen with flax as although once all linen was made from the flax plant at some point the use of the word linen came to mean more a type of domestic item, table cloths, napkins, pillowcases and bedsheets sort of thing most often now made from cotton, rather than the material used. It's a bit pedantic of me but I've been warped by the number of times I thought I'd found the real thing only to discover it was cotton. If you ask for linen now in most fabric shops they will bring out various very fine cottons and cotton / sythetic blends.
The linen I'm using now is pretty much what they were using back then except the looms are now powered. If I was using dyed rather than natural coloured linen there would be a bigger difference although you can get stuff that has been treated with correct period dyes although naturally you'd have to pay more.
I half jokingly offered to make the wife a handloom, our place is a buggered about 18th C industrial unit and the top floor is still a single open plan weaving shed so we have the space but I got the look and backed off pronto. Perversely I could make all the wooden parts, fit the metal ones but actually use it? I'd be hopeless.
Sorry, rambling I'll go and sew some more button holes...
ATB
Tom