The first of those two famine events was handled aggressively by the British administration in Bengal, meaning that the number of deaths from the famine was very small. Lockwood Kipling, who was then living in Bombay, wrote about the local response to the famine in one of the columns attached to the "Famine" tag below.
Some government officials complained that Richard Temple's initial reaction to the Bihar famine was too aggressive and required too much in the way of government expenditure. As a result, under the new Viceroy Lytton, the reaction to the second major Indian famine of the 1870s was much more limited. Richard Temple was sent to manage the famine response, but he appears to have made every effort to ignore the rampant evidence of starvation on a mass scale. Many of the deaths originally recorded in the Madras Presidency listed the cause of death as "cholera," but subsequently historians have pointed out the connection between drought, famine and cholera-related deaths. (One of the columns from the Allahabad Pioneer marked by the Famine Tag below vividly demonstrates the many ways in which Temple and the British administration was attempting to ignore the evidence right in front of their eyes.) Also, see William Digby's blistering critique of Temple's approach to the famine in an excerpt from a book-length study of the famine published in 1878.
The Kiplings did not address famines very much in their writings. Lockwood Kipling only mentions the famine once in Beast and Man in India, and did not address the Madras Famine at all in his Pioneer columns from 1876-1878. Admittedly, Lockwood and Alice MacDonald Kipling were living in Punjab during the Madras Famine, and thus may not have seen evidence of it first-hand. For his part, Rudyard Kipling missed the 1870s famines -- he was then in England. And he did not witness famine first-hand in the formative period of the 1880s, when he traveled widely around northern India as a journalist.
That said, Rudyard Kipling does substantially address famine in one short story, "William the Conqueror." This story was published in a collection called The Day's Work, 1898, several years after he had left India. The famine depicted in this story is set in Madras, and the time period indicated is clearly after the Famine Codes were enacted in 1883. Kipling may have based his account on the 1896-7 famine, which was widespread throughout central India. The focus in Kipling's account is nearly entirely on British civil servants and government workers, who experience great hardships to try and save as many Indians affected by the famine as possible. Some government missteps are acknowledged; at one point the government attempts to distribute grains that are not commonly eaten in Southern India instead of rice. However, it's worth noting that while fever threatens the health of the British government officers depicted in the story, none of the English characters are threatened by the famine itself.
The account of famine depicted by Rudyard Kipling can be contrasted usefully to Pandita Ramabai's quite personal account of the Madras famine of 1876-1878, which led to the deaths of her father, mother, and sister.