Do You have a garden spot? I grow a lot of things for the chickens, but mainly collards, mustard, etc. With Collards---if you have enough plants---when the plants get good size you can break a few leaves a day and throw it to them. Also if you got a fresh tilled place or a soft yard that the grass grows good at----you can use a sharp flat shovel to scoop up pieces like "sod" to carry to them.
What I been doing this year is framing up 4ft x 4ft squares out of 2x6's with 1"x1" 14 gauge rabbit cage type wire over the top. I soften/till up spots in the chicken run---plant things like regular whole corn, rye, millet(in the summer) then lay these 4x4's over the fresh planted spots----then when the green starts growing through the wire the chickens have a lot of greens to eat.
Its kinda funny to watch them at day-light---they go running to these boxes----jump right on the top and start eating the greens that have growed a little over night.
I found that the 1"x1" 14 gauge is the best over 1/2x1/2 or 1" chicken wire or bigger----if its big enough they can get their head through it---they will pull up all your plants---that is also why I use 2x6 instead of 2x4's----it works Perfect.
Oh and the reason I use 4ft x 4ft instead of bigger is so I can easily tilt the boxes out the way to plant more later when needed----not have to remove the wire---just move the whole deal and replace after replanting. A few of these in your chicken run---if you have space---stagger planting them will keep them in greens if you don't have a huge amount of chickens. Just a piece of a bag of whole corn will plant and replant a long time.