The Canadian Flax Council http://flaxcouncil.ca/ is a terrific site for everything you ever wanted to know about flax, flax oil, use in cooking, etc.....

They have a 48-page .pdf format cookbook, NOT lowcarb, but there was a recipe for a vegetable stir-fry, and it called for ground FLAX meal as the sauce thickener, rather than cornstarch. I've worked out the carbs, using Splenda - the whole recipe comes to 11.5 total carbs, of which 5.9 is fiber = 5.6 digestible carbs.
The recipe was for 4 servings, or about 6 cups (when raw) vegetables.

SAUCE:
25 mL ground flax seed 2 tbsp
1 clove garlic, minced 1
15 mL grated fresh ginger 1 tbsp
50 mL chicken broth 1/4 cup
25 mL soy sauce 2 tbsp
15 mL vinegar 1 tbsp
5 mL Splenda 1 tsp

- In a small bowl, combine ground flax, garlic, ginger, broth, soy sauce, vinegar and sugar (Splenda).
- Pour over stir-fried vegetables in wok. Cook and stir 1 minute (or until heated through).

I haven't tried it yet, but it sounds good. I eat a lot of stir-fry. Up till now, I've just cranked the heat up and let the juice / sauce reduce and thicken that way. This, on the other hand, sounds like an excellent way to add a little more fiber to the goods!! ..

Doreen