Initially, anything you plant is going to be at risk until the roots are well established. you can put fencing around smaller shrubs, you can put paving blocks or rocks over the root zones to allow shrubs to get well established. It depends a lot on what you want your yard to look like. Groomed? A walk on the wild side? Are you urban or rural? How much space do you have? Is your yard fenced? My growing conditions are much different than yours, and I live very rural, so my needs and goals may be different than yours. In my yard, I leave a border of weedy growth all the way around the lawn. I've planted an orchard that will enventually provide some cover, as well as food for me, the chickens, and the wild life. I've planted perennials and shrubs/trees that will primarily feed chickens and wild life. Favorites: raspberries, june berries, high bush blueberries, high bush cranberries, elderberries. Apples and pears. Lilacs grow fast. Any shrub that fills in well will be enjoyed by them for shade, and I'm guessing they'll dust bathe under it, as well as use it for safe cover. Check with your state thread to see what plants do well for your chicken neighbors. Check with your local nursery and your county agricultural extension office.
While you're waiting for the plants to establish, give them plenty of artificial cover: several pallets leaning against each other, some hay bales stacked so they can get under them, a table, swing set, any type of lawn furniture, potted plants. You could even erect a pole bean Tee-Pee in your lawn. Provide cover for your flock and harvest some veggies at the same time. I even put fiberglass posts randomly in their run, to clutter the air space in there (before I covered the run.) If they are out free ranging, I will stick posts in the lawn. You can also hang some CD's. They make great sun catchers, sending random flashes of light around the yard. Some folks string fishing line across the yard. A hawk is not going to want to dive into an area where he might snag a wing.