Chickens are not ruminants so they can't really digest very much in the way of hay. A small amount, sure, but not a lot of it the way cattle, goats, and sheep can.
If you want to cut and cure (dry) forage for them then you'd be better off making some sort of legume hay, whatever grows well in your area. They won't be able to eat the woody parts, but the dried leaves and such they may consume.
I use hay with my birds but only as nest box litter. They eat a few leaves of the Coastal Bermuda hay I buy for the purpose, but that's about it. Now fresh young, tender grass they chow down on pretty good.