I'm going to have to go back into my reading to find the article I was reading on flax seed. The whole seed just does not digest well so the dog does not get the benefit of the nutrient they should be getting. Small dogs and delicate digestive systems produce more poo and simply pass the undigested seed out. One researcher was saying they had whole flax seed passing through their dogs.
I do think some companies are putting flax seed in their ingredient list in order to appear as healthy but are depriving the animals of the benefit of the flax.I'm sure it is cheaper to add whole seeds than to process the seed properly. An article about the benefits of flax seed for humans also warns of not using the whole seed.
How Flaxseed Benefits Digestion - Digestive Health Center - Everyday Health
Since neither humans or dogs can digest whole flax seed I see no reason for a dog food company to put them in their food. Little dogs need all their nutrients and whole flax can cause them to pass out more nutrients than they normally would. There are some companies that list ground flax in their ingredient list and I would think that would be much more beneficial and digestible.