May I add whole wheat flour/Chickpea flour to garlic chicken soup?

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.