Flour alternatives for roux

Flour labeled as Cake flour usually is weak flour: low W value, or less formally "low protein" or "fewer gluten". This is somehow weird, as some cakes will require weak flour, whether others nedd strong flour (for yeasted dough cakes, if they add lots of fat/oil to the dough, if they add lots of sugar, pieces of fruits/nuts, etc).

I specifically don't know whether Maida is strong or weak flour, despite this answer and it's comments.

Wheat plants has been selected for several milleniums to get more productive varieties, and, yes, grains that give stronger flour.

Substitutes as weak flour

Trying to get flour from a more "primitive" variety of wheat, such as spelt, emmer or einkorn. These are expensive where I live, and usually sold as bio, but maybe spelt is easily found in India. As they have not been so "genetically selected", they still have less gluten than today's "normal" flour. They also tend to have more and better taste than "normal" flour.

Another flour with low gluten content is rye. It has a different taste than wheat, but I thing it fits really well with cakes. This grain grows better in colder climates, so I'm not very sure how hard will it be to get it where you live.

Other flours, as rice or corn / maize have no gluten. It means gas bubbles won't be trapped in, and will result in a much too dense crumb. You might search some gluten-free bread tricks to solve this.

Substitutes as strong flour

Any bread flour will probably work. Maybe it won't rise as much and you'll get a crumb with a denser consistency, more similar to a "chewing gum" than a "soft cake". But if you are ok with this, you can go on.

Note(Thank to @Anisha for the suggestion): Notice that different flours have different absorption, so some readjustment on hydration should probably be made to the original recipe.

According to On Food and Cooking by Harold McGee, roux functions as a thickener due the starches in the flour swelling up and interfering with the flow of water.

In fact, he indicates that technique can be used with any starch and any fat.

This implies that a lower-protein flour (which implies higher starch, weight per weight) like soft summer wheat, or a cake flour will make a more effective roux.

As an aside: roux can be made with oil instead of butter. As we know oil contains no water, and gluten only forms in the presence of water, we know that roux functions without gluten, as there can be no gluten development in an oil-based roux.

McGee explains that cooking the roux initially increases its thickening power by cross-connecting some of the starches. However, as browning occurs, the maillard reactions are transforming starches and proteins into other molecules, and reducing the ability of the roux to thicken.

So yes, it is true that the darker the roux, the less thickening power it has.

In New Orleans style gumbos, for example, the roux is so dark (almost a mahogony color) that it adds no thickening power at all to the stew—it is there for the flavor. The thickening in that dish comes from (depending on the tradition followed) either file powder or ochra, or both (not considered traditional).

I was not able to determine an ideal ratio of flour to fat. McGee indicates that a 1:1 ratio is traditional. However, if that fat is butter, about 20% of it is water, so that really does leave more flour than fat after the water evaporates. In any case, as long as there is sufficient fat for the roux to be cooked smoothly, it will work fine. Additionally, the fat in the roux is also indirectly an ingredient in the finished dish, so it might be desirable in its own right, depending on the outcome.