It looks like the "plant paradox diet" was developed by an American physician who recommends avoiding lectin-containing plant foods like soy products, grains, beans, and certain vegetables like tomatoes and eggplant. While I'm not a human nutritionist, scientists and dieticians have classified his claims as pseudoscience. 

Even if his claims were well-founded, you need to remember that humans and chickens have different dietary requirements. A major concern I would have with this type of diet for chickens is that they require a fairly high level of protein in their diets (at least 16% crude protein for laying hens, and at least 18% crude protein for growing chicks). It would be difficult to formulate a diet with sufficient protein for growth and production without soy or other legumes. 

For example, soybeans or soybean meal will have 35-45% crude protein, while millet and sorghum typically have ~12% crude protein. Sorghum or millet could be used to replace corn iin a chicken's diet, but you'd still need a good protein source.

In terms of specicic prices of ingredients, it will depend on location and availability. I would recommend checking with local feed mills to see what feeds they produce and what ingredients they are able to access.

If you are just feeding grains, the chickens will have a definite protein deficiency. It is very unlikely they will obtain enough protein from foraging bugs in a field.