I agree with KC. First of all, flax oil is very unlikely to end up stored as fat, or even burned for fuel, because it is composed of EFAs, which your body needs for other functions.

You're right about reaching starvation levels in your body. In fact, you're probably out of leptin right now, and increasing exercise without greatly increasing calories at this point will only make matters worse.

Here's a suggestion that might just kick-start some weight loss--try a low-fat carb-up or even just a pig-out (without watching the carbs) for 2-3 days. As long as you're eating massive amounts of extra calories, your leptin levels will improve and your body will be kicked out of starvation mode.

Of course, you've already said you're having trouble eating enough, but if you cut down on fat (not entirely, but to about 80g a day), you'll be able to eat more.

Then you return to Atkins and see what happens. One note: YOU WILL PUT SOME POUNDS ON DURING THE CARB-UP! Don't worry, it's all water and glucose (=glycogen), and it will all come off a few days after you re-enter ketosis. It isn't permanent weight, by any means.

As long as you're in starvation mode (and when you go back to eating way too few calories, your body will remember quickly), you aren't going to drop much weight, if any.

Sorry to be so long-winded!