I use Miracle Grow on my shrubs all the time, never thought about it; they don't eat the shrubs but they certainly scratch under them (I gave up on mulching them.)
You would not want to put out a granular fertilizer on your lawn and turn them loose. You could probably water it in or do it before a heavy rain, and let them on it after it was rained in or well watered in, if it dissipates. You do not want them eating the granules.
If you turn them loose in your veggies, they will eat most of the veggies and young plants. The one thing chicken wire is good for, in my experience, is to fence them out of the garden. I'm not much on flower beds but have read on here of people having trouble growing flowers that chickens can get to, as well.