What are the conflicts in "Shooting An Elephant"?

The most obvious conflict in "Shooting an Elephant" is the narrator's unwillingness to shoot the elephant that went on a rampage. This conflicts with the perceived need for him to do so as a display of colonial strength and resolution. In other words, he is conflicted over killing a now calm and non-threatening animal for no other reason than to save face. The narrator knows that shooting the elephant will cause it to die slowly--an elephant is difficult to kill--and in pain. He knows there is no real reason to inflict suffering on the creature. He also understands that if he doesn't do it, British authority will be undermined, and he will be viewed as a weakling by the Burmese, who expect him to shoot the animal. 

Beneath this lies the more universal conflict brought on by colonialism: the Burmese people hate their British overlords for their violence and coercion, will undermine them in any way possible (a rebellion will occur a few years after Orwell leaves), and wish these unwelcome masters and conquerors were gone. This forces the British into controlling the Burmese through ever more violence and coercion, as there is no sympathy between the two groups. Orwell's point is that colonialism creates systemic evil in which the conflicting sides, the oppressor and oppressed, both play out destructive roles. The Burmese won't respect the British without gratuitous displays of power; the British are forced into acts that inflict needless suffering in order to maintain power. The narrator experiences a further conflict: he both hates the Burmese for their passive loathing of him and yet hates the oppression he has to enforce as a member of the British police force.