"Flax seed, quinoa, and other seeds and grains are often described as having a nutty flavor and/or aroma. Does that mean I should not serve them to someone who has a nut allergy?"
A food can taste and smell nutty without actually containing nuts. For example, when butter is cooked until it is brown, it gets a flavor and aroma which is often described as "nutty".
Having said that, however, I must also warn you to be very careful, depending on the severity of the allergy. Flax seeds may be processed in a plant that also processes nuts. If the package does not state either way, contact the company to see if the product in question is processed in a nut-free environment.