Barley: late June, early July.
Wheat: August (fall-sown wheat and Kamut can usually be harvested in early August). To thresh, the seed kernels should be hard enough that you can't make an indent with your fingernail: if the grain is too soft, let it dry out in a greenhouse or a dry, hot place until it's ready.
Rye: July for fall-sown rye. We haven't tried planting rye in the spring for harvest so don't know how long it would take to mature.
Flax: early August. Shake the stalks and you'll hear the seeds "jingle" in their spherical seedpods.
Buckwheat: late September.
Amaranth: "when the birds start pecking at your amaranth plants, it's time to harvest," says Dan Jason (i.e. late September). If you leave the seed on the plant too long, they will harden and it will be extremely difficult to thresh. Shake or rub the seed heads to loosen the seed into a bucket, then dry the seeds indoor on trays for at least one week. When they are rock hard, they are ready to thresh.
Quinoa: September/October. Feel the seed heads: if the seeds feel like hard balls, they're ready to harvest.