I've drunk it for over two decades and never seen it "chunky". It is slightly creamier like a full-fat milk or a tiny bit more. Almond milk's kind of a perfect medium for my liking. Rice milk is almost always thinner like a 2%, and you usually do have to shake that one a bit more. Coconut's the one that's most noticeably different from the cow stuff, it's okay on cereal but better in a blend.
I actually think an almond/soy mix is kind of the perfect blend. Even if I weren't vegan, I don't think I could (a) either get used to the concept again, or (b) reacquire the taste for the cow stuff any more :-/