I think this is not such a good idea. It is going to take a lot of nutritional yeast to get anything like the thickening power of flour. If you really want to thicken this with less flour, there are plenty of other things that will do the trick, like xanthan gum, potato starch, corn starch, ultra-tex, some formulations of methylcellulose, etc. Just add however much nutritional yeast you want for flavor or health reasons, and get your thickening elsewhere.
My guess would be that you boiled the soup at some point, possibly for an extended period of time.
If you bring it to a full boil the fat from the meat will emulsify and distribute itself through the liquid. This is the same stuff that foams to the top, the "scum" that a lot of recipes (usually ones that say bring to a boil, then simmer) tell you to skim off. I would venture to say that this distribution of the fat into the liquid is also why it tasted heavier.
When making stock or soups, the most I'll heat them is to just below boiling and keep them at that simmer for a little longer to make up for not bringing it to a boil. When making stock, I strain once through a chinois and again through a piece of cheesecloth in a chinois to help reduce the floating particulates, but this won't really solve the cloudiness problem (though it will help some).
You can also try putting it into the fridge overnight so that the fat comes to the top and solidifies, but I don't think this will solve the problem, only help reduce it.
If it's just the stock that's gone cloudy, this page has some suggestions on how to clarify it, but honestly unless you're presenting it to guests, I see no reason to even bother. I've made cloudy stock and clear stock before and except for a slight "heaviness" difference, the taste is generally about the same. The cloudy stock sometimes has a more oily mouth feel, but it's not a major difference - and I've found some people seem to prefer the soups or rices I make with a cloudy stock.
If you have a hard time controlling the temperature on your range-top, you can use an oven-safe stock pot and cook it in the oven at 180°F to keep it just below a boil.
One other trick, depending on what kind of soup you were making - if you were making (for example) chicken soup, consider trying to turn it into a cream of chicken soup to hide the cloudy broth :)
Best Answer
This gets simple when you consider what the flour is used for:
You create a roux, which then thickens the soup. The starch in the flour is altered during the cooking process and then binds the liquid.
You can use any kind of flour that contains starch, but depending on the starch-to-other-components ratio, you might have to use a bit more for the same thickness. Unlike for baking (gluten!), chickpea flour will work fine in a roux. Also, a non-white flour might be visually less appealing because the external parts of the grain may give the soup a greyish or speckled appearance. Note that the less refined your flour is, the more it might influence the taste of the soup. But whether this matters obviously is a question of personal taste.
The choice is yours:
A few tablespoons of white flour in a pot of soup probably won't compromise your dietary regimen, but it's probably not worth going out to buy a whole bag for a single use.