I would think a 1" diameter branch would be right for bantams, so 3 cm sounds good. I don't know about the flat part. You could try rounding off the edges. It would probably be easier to just go cut a straight branch and put that up than to try and round off the edges of a small diameter...
If they have small chicks with no juvenile feathers, it would be natural for them to stay with them on the ground. If the chicks can fly/jump, here is what I would do:
Go in at night. Find the bird you think is the flock leader. Pick that one up and put it on the perch. Once that one is...
How high is your roost? From 3-5 weeks old, my chicks never much used the roosts in the brooder, they were maybe 2" high. However, the first night in the coop, about a dozen used the 2' high roost. The next week, about 16 were using the roost. The next week it is 20 of 25.