SATR, have you tried looking for linseed? It's the same thing, just different name. Can't get flaxseed in Australia either - it's sold as linseed here. We have a very similar climate to yours, hence merino sheep and cane toads [idk what they're called in South Africa but that's where they were imported from] have done amazingly here.
I'm presently feeding a coat supplement called Omega Maxicoat, which is I think a mix of kinds of seeds that give the horse what it needs for an amazing coat, and my gelding's coat is really nice. Unfortunately I can't give it to my filly because she has either food allergies or extreme protein/carb sensitivity and goes lame on certain feeds. I don't groom all that much, I haven't clipped anybody yet, they do have rugs on at night though.
Recently I washed my lad in human shampoo and then used human conditioner on him. Some horses can't cope with that and come up in allergic reactions so do be careful and patch test first - but his coat came up SO soft and shiny! And his mane and tail too. I don't think his mane and tail have felt so nice... ever... they're kind of coarse but they feel gorgeous now. So, if you DO have to bathe your pony, condition him! It replaces the natural oils in the coat. Or use a shampoo that doesn't strip them in the first place. That sort of thing -is- available, but more for people than horses.
My horses are both on hoof supplements as well as coat supplements, by the by :) one has really bad, shelly walls [really hard soles though, and his feet aren't that bad allround, just gets cracks and chips really bad no matter how short I keep him] and the other is a young TB so proper nutrition to feed her hoof development is super-important. Plus the hoof supplement can have the side-benefit of assisting with minor joint problems, and my filly has a stifle-centric, feed-related lameness that is completely gone at the moment because she's on the right feeds for her. [I feed Biotin and the bucket says it's good for coat, cartilage and hooves... I also feed MSM which helps with biotin absorption and is good for... guess what... "cartilage, skin, hair and nails" - mine is supplied for cheap by a company that refines it for human consumption]