If foreign-produced flaxseed oil costs 20% of US-produced flaxseed oil, and is imported in quantity, "What happens to the market clearing price of US-produced flaxseed oil?" is not a very difficult question. We do not need to adopt the counterfactual "Consider what would happen to flaxseed oil prices in an American city which banned foreign flaxseed oil. Why, they'd be a laughingstock! Flaxseed oil consumers would flee to other jurisdictions!"

That's an interesting speculative conclusion to a hypothetical policy that is not on the table nor will ever be considered in the United States. Back to the question: what happens when you import cheap flaxseed oil? Market prices go down, with very high confidence. Claims to the contrary would generally require fairly persuasive proof since they invert our understanding of how the world works.

(n.b. I don't particularly think my political opinions are relevant, in much the same way a physicist doesn't feel the need to mumble "Sorry to be a gravitationist" prior to suggesting that a banana pushed off a table will tend to accelerate towards the ground rather than hovering in midair, but to the extent I have them they're "Let the flaxseed oil flow" and to the extent I have economic interests in US-produced flaxseed oil I'd prefer it to be as cheap as possible since I'm a buyer more than I'm a seller.)