If they are just digging in the beds, you can put stepping stones or other barriers around the flowers to keep them from digging. But if they are eating the flowers, then I don't know of anything you can do to keep them out other than a fence.
single, or double wired electric fence works the best... not as noticable and tacky, and doesn't look as shabby as chicken wire strung all over the place. also not as expensive, or perminant as "pretty" fencing.
I think you will have to put up a barrier if you want to keep them out. I think the garden is like a smorgasbord for them. I let mine out of their run for an hour or two in the evening, and it seems to minimize the damage, however I did wait til the summer after my plants had established themselves too. I think that keeps them from totally destroying things, but man! They sure do like to EAT!!
I have bark surrounding the flowers and they dig huge holes in the bark and cover the plants with dirt and bark...and have almost completely dug up a few plants.
Yes, you'd need to put flagstones or similar down instead of bark. Not gravel, but larger rocks. They won't be able to dig up the roots. But they could still eat the plants if they are tasty.
For many years I had a nice flower bed of deer resistant plants surrounded by rocks, boulders, flagstones etc., and I had bark scattered around the rocks. It held up well despite their abuse. They left most deer resistant plants alone but not all, it took experimenting. Some are poisonous so use your judgment. I've had to protect tasty plants like my veggies and blueberries with fencing. Eventually I planted too many edibles to protect the plants from them, so no more free ranging
. I plan to get a pasture pen / large tractor for occasional grazing, though. I found that younger chickens are much more destructive as they sample everything over and over before deciding it tastes bad.