From Natural Attacks Description:
Most creatures possess one or more natural attacks (attacks made without a weapon)
So, not, natural attacks are not a weapon. They can't be enchanted as weapon, they don't receive bonus for weapon enhancement spells etc..
So the "He takes no penalty for using multiple weapons when making a flurry of blows, but he does not gain any additional attacks beyond what’s already granted by the flurry for doing so" statemente only prohibits to gain aditional attacks from two weapon fighting or similar effects (as that "for doing so" referring to using multiple weapons states)
