Whitney only appears in the beginning of the story. In order to figure out the purpose of this character, you need to examine the contribution that he has to the overall story. What does he say or do that ties in to the Main Character, Rainsford, or to the themes of the story.
Look at the conversation that Whitney has with Rainsford about hunting. After Rainsford comments about Rio having the best sport in the world, Whitney corrects him by stating "For the hunter. Not for the jaguar". To which Rainsford asks, "Who cares how the jaguar feels", and Whitney responds that "Perhaps the jaguar does".
This conversation continues and opens up the issue of hunting and the morality of its undertaking. Whitney also serves to introduce the background for the upcoming setting of "Ship Trap Island".