evening primrose and borage both contain GLA (gamma linoleic acid) while flax contains ALA (alpha lineleic acid). Both are good in different ways and I take both. I take borage because it has a higher concentration of GLA. I believe you've heard no evening primrose oil for babies because of it's estrogen-like effects (it's helpful with menopause) but borage doesn't do that. You should be taking some of each (ala and gla) to get a balance of oils.
Borage oil is only 1/4 teaspoon for an adult, so I assume the amount for a baby would be really small. I take the oil and it's very mild tasting. There's also a brand (refrigerated) that makes a blend of these oils just for kids! I can't remember the name right now but it's in Whole Foods. Even if she doesn't like the taste, she won't really be able to spit out 1/8 or 1/16 of a teaspoon of oil, which will coat her mouth.
Cod liver oil, which I don't take because I"m vegan, has DHA, another one of those acids. Your body can't make this on it's own but it can make it as long as it has proper levels of ALA and GLA. Because I take both, I don't worry about my DHA supplementation and my eczema has completely gone away just from those two. If you're worried, take a little CLO just to be safe.