You can use plain yogurt, but it must be strained first or it will not work. Strain it 6-8 hours using cheesecloth. The point of the milk product is as a carrier for the flaxseed oil; the importance is less what type, but how well it performs in this capacity. Unstrained yogurt has too much whey.
Once the flax oil/yogurt mixture is completely blended (takes at least a minute or so) and you've stirred in the freshly-ground flax seeds, you can add all sorts of thing as the previous poster said, from sweet (fruit NOT sugar!) to savory to improves the taste. Just make sure to down the entire amount of the mixture each time. I too hate the taste of the flax oil as I taste bitter things exceptionally well. However, the whole seeds when fresh should taste nutty. You may have got rancid seeds. They are very cheap so try replacing them and see if that helps.