You’d be looking for dogbane, not flax. Flax is middle eastern, doesn’t grow wild in New England, and is pretty much inferior to dogbane ayway for the stuff we’re doing.
Velvet leaf, cattails, milkweed, and the bark of some trees work well, too, esp. since dogbane is a mostly-spring sort of thing, but that’s probably more detailed than we want our game to go.
Have a generic “fibrous plant” that grew commonly in, say, swamps (and maybe far less commonly in forests) would be nice, I think. Basically add cattails and the various swamp milkweeds to the game as a primary fiber source.
Finally! A reason to visit swamps!
Note: Velvet Leaf isn’t native, but it’s certainly found here now. It was actually brought over as a fiber crop, and promptly became an incredibly common weed.