I've never had a case of impacted crop in my flocks. I think long, coarse, dry hay is more of a concern. Fresh, tender greens have never been a problem, here. They usually just pluck the tender leaves from alfalfa.
We have clover planted, also. I also plant extra greens for them. The chard handles warm weather, as well as cold. It handles our short springs here and I always plant a lot for us. The mixed colored type is pretty, too. They also have a selection of things like kale, leaf lettuce and other dark leafy greens. They like chick weed and various things that grow in the wild areas of the property. Lawn grasses or grasses from cereal grains are eaten, like wheat, oats or barley. They like all kinds of berries, tomatoes, as well as other fruits and vegetables. I usually grow some cherry tomatoes for them.
You can also plant things that will go to seed, like sunflowers, amaranth, etc.
In the warmer months, they pretty much just forage on their own. I plant things for them that they can forage on and also have other things that are in our garden, that they don't have access to, for obvious reasons. In the winter, I offer sprouts and wheat or other grass that I've grown.
In a small yard or for confined chickens, you can plant pots or garden flats of things to give to them. You can also fence off a little area and only give them access when the plants are large enough.
GrowOrganic.com has a lot of pasture mixes. They have one for chickens, that you can buy by the pound. You could look at that. For people with only a few chickens, you can even just use sprouting seeds for some things. It's expensive for a pasture, but not for just a pot or only a few alfalfa plants. Plus, it lets you try it out, as an idea.