You will noticed them fly around then all of a sudden fly across the pen at each other,probably jumping around and pecking each others faces.The older they get the more violent the fights can get(It generally starts all fun and games until some one gets serious,lots of times pullets just play fight and whoever ends up being strongest usually ends up being boss,but this squally takes a few weeks to determine I have noticed),never have had any serious fights,but will say cockerels tend to be more prone to fight harder and actually cause blood shed,even as very young birds,I have also noticed roosters get more butt hurt or threatened much faster then a pullet,guess they have some major anger issues.
Usually the first few days your probably not gonna notice much fighting but a ton eating.By week one they should be flying /running from corner and corner and having a blast and probably fighting aback and fourth.
I have another pecking order question. My friend has 4 full grown rescue chickens in which she got in the winter that are Rhode Island Reds and Rhode Island Red mixes. The one lowest on the pecking order started getting pecked so much near its rear in the same spot, that it started to scab and create a bald spot. Should they be overly concerned?