Secale multicaule is a rye-typ for a two year growing cycle. Traditional sowed around the 24. June, but you can sow also in spring or fall, it is mown before it sets on the grains in the first year, in the 2. year it is cut like the normal rye.
It not only doesn't need crop protection products or artificial fertilser it doesn't tolerate the chemical stuff.
It grows 2 meters high and has many small but deep roots, so it is great for cultivating a new patch or as prep for vegg.
It is a good sorce for green feed in the first year, but as a rye-typ it isn't good for chicken feed in the 2. year but many organic bakeries work with it b/c it is sweeter than the normal rye, has more protein and deeper colour.
But still... you can let them hunt in the patch b/c it's 100% chemical free.
Buckwheat is not a sweet-grass it is a knotweed and the only other crops that are related, I think, is rhubarb and cotton. So you can grow it before and after almost all other crop without risking cross infection by plant diseases or bugs. I has a very short growing period form 10 - 12 weeks and grows well without fertilser even on acidic and sandy soil. A patch with buckwheat is not only an eye candy it will bring bees into your yard like only a few other plants, so it is a good neighbour for everything that needs a pollinator. And if you plan to keep some bees... they make a fantastic dark honey from the white-pinkish flowers of the buckwheat. It grows so fast that summer weed has no chance and so it "cleans" the patch for other crops. You can mow and thresh it. The little dark grains are rich in protein and your chicken will love it. If you want to use it as food for yourself, you should peal it, most coop mills can do that here but o/c they would do it only for bigger quantaties than I want/can produce on my allotment.
Harvesters are very expensive, so maybe you should learn how to hand mow with a scythe or use a sickle bar mower,.... some lawn mowers can be aquipt with sickle bars.