The short answer is, nope.
There are a couple of things you can try, but with chickens and flower or vegetable gardens there is never any guarantee. I'm assuming if you've already winter mulched the perennials, the heads and stalks of the flowers have been cut back. If so, you can try what we did, although I readily admit we had mixed success.
We got out the chicken wire (at last - a use for those rolls we bought way back when!) and laid it flat down OVER the entire bed, overlapping where we needed to and pinning where we needed to with landscape fabric staples and bamboo stakes. We did this right over the mulch last fall. I will say that it was a great help keeping the leaves we covered the beds with in place and not blowing all over the place when our winter winds hit. Despite freezing and snow, the winds here are still strong enough to blow the top layers off, so that was an unexpected bonus. The girls didn't like walking on the chicken wire, and couldn't scratch through it anyway. But they always tried. It did also keep out rabbits, which was kinda nice.
The other thing you can do is the one solution you don't seem to be in favor of, and that's fencing. Good fencing make good neighbors - or in this case chickens. We found that if we used a decorative fence, they happily leaped right over it and went back to work. If we used a tall wire welded fence, I frankly thought it looked kinda tacky and wasn't afraid to tell hubby so - repeatedly. That's when we went to the chicken wire stretched out flat over the beds. As I said, it kept them from scratching in it but didn't keep them out of it completely.
Good luck with whatever you decide to do. Hope that someone chimes in with better ideas - I'm all ears too!
