Do natural armor bonuses stack with itself from multiple sources in Pathfinder?
Natural armor bonus is a type of bonus that does not stack with itself (like most bonuses). If you have a +1 natural armor bonus from, say, race, it will not stack with the natural armor bonus granted by another ability.
Certain abilities, like the barkskin spell or amulet of natural armor, specify that they grant an "enhancement bonus to the creature’s existing natural armor bonus." This means that you increase your natural armor bonus by that amount, before adding the total natural armor bonus to your AC.
Note that multiple enhancement bonuses to natural armor will not stack with each other. Only the highest one applies.
(Magic armor works the same way, by adding an enhancement bonus to your armor bonus, then adding the total armor bonus to your AC.)
No, natural armor bonuses from multiple sources do not stack. From the Pathfinder SRD:
A natural armor bonus improves armor class resulting from a creature’s naturally tough hide. Natural armor bonuses stack with all other bonuses to armor class (even with armor bonuses) except other natural armor bonuses.