In "Animal Farm", how do the pigs gain the rights to the cow's milk? Why do the animals allow this? What does this event suggest about the power...

The pigs gain rights to the milk simply by saying that it is their right.  The important thing that this suggests is that, althought the "personages" have changed, the rules of power still remain in play ... it abhors a vacuum.  It also suggests that most "people" are in fact sheep and are easily susceptible to propaganda.  What ultimately is suggeted is that the state of the animals on the farm will, in the long run, not be much different from their initial state.