What is the conflict and the theme?
The conflict in Rikki-Tikki-Tavi is between Rikki, the protagonist, and the snakes, the antagonists. As stated in the first paragraph of the story, the conflict is a "great war." It is, in fact, a life-or-death struggle between Rikki and each snake he meets.
There are several themes that come through in the story. First, Rikki's courage despite his youth and size emphasize the theme that even the young can stand up for what's right and fight against evil. Rikki's courage comes from his natural ability, but also from his firm conviction that snakes cause harm and devastation. Rikki confronts Nag when he first meets him, saying, "Do you think it is right for you to eat fledglings out of a nest?" The snakes represent a threat not just to animal life in the garden, but also to human life in the bungalow. Rikki overhears the sinister plans of Nag and Nagaina as they plot to kill the child, Teddy, and his parents. The cobras' motivations are nefarious; they want power and control, and they will kill to get it. Thus Rikki's battle against the snakes can inspire readers to stand and fight against evil, even if they are young or small.
Another theme that comes through in the story is that one should be humble when taking satisfaction from a job well done. Rikki spurns Darzee's foolish song of praise, preferring to focus on completing his work rather than listening to accolades. But when Rikki has disposed of Nag, the eggs, and Nagaina, he flops down in the grass for a well-deserved nap. He is satisfied with his accomplishment, but as the final paragraph states, "he did not grow too proud." Thus the story communicates that a job well done is worth savoring, but not worth boasting about.
Rudyard Kipling wrote an entertaining story with a life-or-death struggle between good and evil that spurs readers to have the courage to stand and fight for what's right and to take satisfaction in their work without undue pride.
The main conflict of Kipling's enduring short story is Rikki's inevitable battles with the cobras, Nag and Nagaina. Rikki is aware of the cobras' deadly abilities, but his natural instinct takes over on two fronts: A mongoose's mortal enemy is the cobra, and his own fears become secondary when one is near; and, his other duty was to protect the human family which had befriended him. His own safety was less important than these two instinctual urges.
The story contains several different themes. Courage vs. fear is one. Man vs. nature is another. Kipling's military background focuses on the importance of loyalty and duty, and the Darwinian theories of the survival of the fittest is yet another example.
The might of the British Empire vs. the simple ideals of Indian culture is another theme. It expounds Kipling's belief of the superiority of the white man (represented by the British family as well as Rikki) over the Hindu people (symbolically epitomized by the evil Nag and Nagaina and the cowardly Chuchundra).
Or you may want to refer to the enotes theme link below.