Information to consider:
Amaranth is a relative of pigweed, as is quinoa. A site said they may contain excessive levels of nitrates, but I recall that all those plants, as well as parsley and carambola (star fruit), and moringa tree leaves, contain high levels of phytic acid, which is referred to as an "anti-nutrient".
Phytic acid binds with nutrients, including calcium. If it binds in the gut, it forms mineral salts that are sharp edged enough to cause problems in the intestines, and if it binds in the kidneys, especially with calcium, it forms kidney stones. People who are prone to kidney stones seem to have more problems with this.
However, what is harder to find as you research is that phytic acid also binds with toxins, helping move them out of the body, which can decrease problems for long term health. Foods that contain it are associated with reduced cancer rates and reduced major organ problems.
It is a balance and only you can decide if it is something you are willing to do. Interesting is that all these plants are very high in nutrients, so loosing some nutrients still leaves plenty to be utilized. With Moringa, i saw a study where the chickens did fine using dried leaves as up to 10% of the feed. After that, the chickens started loosing some small amount of weight, laying slightly less, and eating more.
Fermentation reduces the effect of the phytic acid more than does blanching according to another study.
Notably, oats also have high phytic acid which according to yet another study is unaffected by fermentation...
Also, nitrates are a problem in even ordinary benign plants during drought conditions according to an agricultural report.
My chickens main food is raw rolled oats and they are all healthy, lay perfect hard shelled eggs six days a week or more, and have never been sick. They are slim, but I see that as a bonus to prevent weight related problems with laying, organ damage, as well as heat tolerance issues.
I had hopi red dye amaranth in my garden last year and the chickens did not eat the leaves: Showed no interest in them.
I had to fight to keep them away from the tomatoes, though... Those leaves also contain phytic acid.
The last thing to consider is that a lot of chicken feed studies are focused on biggest short term gains at the least expense to commercial producers of meat and/or eggs. These birds have short lives, unlike many of our chickens which are kept for their natural livespans.