What conflicts in general does Napoleon deal with?

There are a number of conflicts in Animal Farm—the animals versus Mr. Jones, Snowball versus Napoleon, the common animals versus the pigs, Animal Farm versus the neighboring humans—but all of them are expressions of the underlying tension between the exploited and exploiting classes and between the lofty ideals and harsh realities of socialism.

After the story's climax in Chapter V, where Napoleon runs Snowball off the farm with his trained pack of dogs and declares that all decision making power will be exercised only by the pigs.

Squealer comes to the forefront in order to justify Napoleon’s actions with skillful but duplicitous reinterpretations of Animalist principles; Napoleon continues to consolidate his power, eliminating his enemies and reinforcing his status as supreme leader; the common animals continue to obey the pigs, hoping for a better future.

Napoleon's biggest inner conflict is trying to make sure that everything the pigs are able to take control of is in essence a collection of power for himself.