I have 3 Chickens in my garden. They have a Shed approx. 8 feet x 4 feet and their enclosure measures approx. 36 feet x 25 feet. The enclosure is well planted with Trees , Hedging , Shrubs, Perennials, etc. ,with plenty of places for dust baths, etc. Most evenings, I let them into the main garden for an hour or so ( easily judged by the light level) so that they can have a good peck about on the lawn without destroying it.
As Chickens naturally scratch up the earth, the major damage they will do to plants is to expose the roots. However, they are extremely useful for turning over your compost heap.
Consider all the aspects before taking the plunge
Fresh Greens ( bunched Spinach or Cabbage leaves for example ) tied to their perimeter fence every day is appreciated particularly if they don't have access to fresh vegetation in their enclosure. Trying to make and keep a "lawn" for Chickens in a restricted area is MHO a waste of effort.......if they are constantly on there, they will just ruin it.
Many people seem to make the basic mistake of keeping Chickens when they really do not have the space to keep them properly. They are no different to any other "pet" if you intend to keep them on an amateur basis.