I don't know for sure as I have never grown flax, but some seeds require freezing to germinate well. Snapdragon is one like that. It may also be that it likes to germinate at cooler temperatures. If Flax comes back from self seeding and not from starting saved seed in warmer weather or inside, it just may be one like that.

The best way to do it is just like the plant would do naturally, so yes try planting it in the fall and see what happens