Flax is one of the oldest plants to be grown for fibers. It has small seeds that can be eaten by themselves, e.g., in salad, and linseed oil (also called flaxseed oil) is made out of them. Linseed oil can be used in food, but is not very common, I believe.
I have not been able to locate a lot of information on the web about the status of flax seeds or linseed oil on Pesach. On the one hand, flax seeds are seeds just like so many other seeds that are commonly regarded as kitniot (e.g., sesame, mustard, poppy). I believe flax was known in the 13th century and supposedly they ate the seeds as well. I am not sure if flax seeds might get mixed with grains of chametz. On the other hand, flax seeds are not made into flour or used like grain in any other way. So, it might be doubtful if flax seeds are kitniot, and that might be enough to permit linseed oil.
So what do the lists say? The Star-k contains neither flax seeds nor linseed oil. The cRc Guide states explicitly that "Flax seeds are not kitniyot". The OU lists linseed in the category "The following are not considered Kitniyot, but may require special checking". Kashrut.com writes as a comment on flax seeds "this is cosidered to be acceptable by some rabbis and kitniot by others".
- Danger of chametz traces: Don’t think so.
- Danger of confusion with chametz (raw): No.
- Danger of confusion with chametz (processed): No.
- Botanical categorization: Linaceae.
- Known in 13th century: Yes.
- Verdict: Don’t know.
photo (c) Sanjay Acharya