Just to clarify:
At the beginning of a round, before he acts, is an Uncanny Dodge Barbarian still flat-footed?
What's the rule here: does he lose this bonus because you are denied your DEX bonus at the start of a round?
Fred
Uncanny the barbarian is flat footed, so he can't make attacks of opportunity. He however maintains his dexterity bonus to Armor Class, so he cannot be sneak attacked because he lost initiative or was surprised.
At the beginning of a round, before he acts, is an Uncanny Dodge Barbarian still flat-footed?
Flat Footed Characters with uncanny dodge retain their Dexterity bonus to their AC and can make attacks of opportunity before they have acted in the first round of combat.