I do not exactly get a point here. For example Harpies are monsters which can fly so all the rules for flyers and monsters and writen exceptions apply. Birdmen are infantry which can fly so all the rules for flyers, infantry and exceptions apply.
So for all flyers first of all all flyers rules apply. Command range, limitations for terrains, movement range, homeback and so on. Then all the monster/infantry rules apply: additional attack, support etc. Then exceptions: cannot have characters, can be pursued etc.
What exactly is not clear in the description?
Please remeber that in WM there is no unit type: flyers. There are monsters who can fly or Infantry in this case. Anyway if re-writing these rules I would certeinly opt for removing the support option for Birdmen. There are too few of them in the unit. But for now it is clear for me, they can get and give support because they are infantry. They cannot move into woods because they are flyers etc.