I do not care whether they are round or flat, I do think they should be wider maybe a 3-4 inch diameter. Chickens roost but they are not perching birds. Chickens can perch, but it is not their natural state. IMHO. Also in cold wet temps you want the chicken to settle down on its feet to keep the toes warm. They cannot do that if the diameter is too small.
I am feeling for you Energizer. I get the feeling you think we are "picking" on you when we offer other suggestions. Trust me that is not the case, we are just trying to help you not make the mistakes many of us made. There is no doubt the chickens can get by on the branch you put in there.
We just think it could be better than getting by for the birds. I cannot tell you how many of my birds, mainly chicks< have died because I misread something they did, had or needed.
Hang in their your doing good, and do not stop asking here. You might want to join your state pages too, they have lots of ideas that work in your area. You can also get to meet some of them. In our state thread we have become a pretty tight bunch and actually see each other in person once in a while.