Flax flowers are one of the items sold at airport shops when your city is in first place in Conquest standings, at a price (if I recall correctly) that is less than half of the guild price. If you don't have access to the airport shop (either because you are not Rank 5+ or because your nation is 2d or 3d in the standings), just ask a qualified friend/LS member/etc. to purchase them for you. When I was doing this level, I bought probably 30 stacks of flax flowers from the Bastock airport shop at once, since I correctly assumed that it was such a rare occasion that Bastock was in first (one week, several years ago, lol) -- but it allowed me to make a healthy profit at this level of clothcraft, and have enough linen thread to make all the linen items thereafter. Good luck!