Unfortunately it's not really about the "eating," it's about the SCRATCHING. Like slow motion I've watched my helpless little seedlings crying out as they leave the dirt to fly through the air and die. Unless you can shackle and chain your chicken's legs (not a good idea,) you can't stop them from digging up your plants. They're not rabbits and they'd way rather eat all of the bugs and worms in the soil the poor unsuspecting plant is trying to grow in. Wire cages around plants and of course a wire fence around your garden is really the only way to go.
Also - I have a decent sized veggie garden with fencing around it. But I also have a rock garden where instead of wire fencing it, I put the wire directly on top and let the plants grow up through it. They still manage to kill alot of it, but some of it stays protected from their digging feet due to they cant dig through the wire. You could try that but I think with Veggies in particular they're going to just eat and/or peck the plant itself.
Take the weeds and plants that are safe for chickens to eat, and dump them in the run. Let the chickens scratch to their hearts' content. Later, harvest the wonderful compost they have made for you.