Although flax seed oil is often recommended as an omega-3 supplement for children, there is a problem. Flax seeds contain the omega-3 fatty acid ALA that must be converted to DHA by an enzyme so that the body can incorporate it into cells. Children make this enzyme only in small amounts, if at all. If they do not have the enzyme they will not benefit from the omega-3 fat in flax seeds. Newborns are completely unable to convert ALA to DHA. A study of breastfeeding mothers who took a flax seed oil supplement had no resulting increase in their own plasma or breast milk levels of DHA, showing that adults do not make this conversion either (Francois et al., 2003). Flax seeds are not an adequate source of DHA.
I recommend that children and adults take a fish oil or cod liver oil supplement. Cod liver oil has the added benefit of vitamins A and D, especially helpful in the winter months when sun exposure may be inadequate to provide enough vitamin D. An alternative omega 3 source for vegetarians is an algae-derived DHA supplement (trade name Neuromins).
You can find a more complete omega 3 discussion at this link.
Francois, CA, et al. Supplementing lactating women with flaxseed oil does not increase docosahexaenoic acid in their milk. Amer J Clinical Nutrition 2003 Oct; 78(4):164-167.