 This phase III trial studies the side effects and best dose of entinostat when given together with aldesleukin and to see how well this works in treating patients with kidney cancer that has spread to other places in the body. Entinostat may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Aldesleukin may stimulate the white blood cells to kill kidney cancer cells. Giving entinostat together with aldesleukin may be a better treatment for metastatic kidney cancer. 