Okay, technically yes, you can fry things in flaxseed oil, but it's fucking stupid. The oil is very fragile and extremely expensive. You shouldn't even buy flaxseed oil that's been stored unrefrigerated.
The entire point of paying (on average) $0.75 per ounce is to get the health benefits. You can find many, many other oils that are much less expensive for cooking. Flax oil should be used like a condiment. If your flax oil doesn't have a sweet, nutty flavor that would make it a nice accompaniment to a dish then PITCH IT, it's rancid.
But don't take my word for it:
http://www.barleans.com/faqs.asp
http://www.askdrsears.com/html/4/T041700.asp
http://www.vegfamily.com/vegan-children/flax.htm