Ziegfeld Follies were a Broadway show that ran in New York City from 1907 through 1931. They became a radio program in their own right in 1932 as The Ziegfeld Follies of the Air. It ran until about 1936 and Rogers did occasionally make a guest appearance. KDKA wasn't exactly new, it had been on air as 8XK as early as 1916. Founder Frank Conrad received the call letters KDKA in 1921. This was a pivotal time in radio history. Radio was a new medium, and really before 1922, it was just a hobby. Will Rogers arrived in that crucial window when radio was first able to create national celebrity. More on KDKA here.
He started making his first regularly scheduled broadcasts in the spring of 1933. His program, The Gulf Headliners was sponsored by the Gulf Oil Company. Also called the Good Gulf Show was broadcast from 640 KFI-AM in Los Angeles. It ran for half an hour on Sunday evenings and by 1935 was ranked nationally among the top fifteen radio programs. It was said that he often lost track of time and was often cut off in mid-sentence. To compensate for his wandering mind, he brought in a wind-up alarm clock, cued him to wrap it up. By 1935, the show was sometimes referred to as "Will Rogers and his famous Alarm Clock." There were a total of 53 episodes.
Technically, it was actually his second try at a weekly radio series. Previously, the pharmaceutical company Squibb had sponsored a series of 15-minute monologues at KFI-AM in April of 1930. There were only 12 broadcasts before the series ended.
But getting back to the Gulf Headliners, its popularity led to certain problems. In January 1934, Rogers used the word “nigger” in a radio skit, referring to a song as a “nigger spiritual” and possibly up to a total of four instances. This was not the first time he'd used the word, Rogers had used it in print in his syndicated newspaper column as well.But this was the first time he had used it on the radio. Roy Ottoway Wilkins at the NAACP launched a telegram-and letter-writing protest campaign against the comedian. In response, Rogers switched to the marginally less offensive term "darky." (It sounds pathetic now, but prior to the civil rights of 1964 you could honestly call that a victory)
Rogers died in 1935 with aviator Wiley Post, when their small airplane crashed near Barrow, Alaska Territory. He was 56 years old. For more information, I recommend the book Radio Broadcasts Of Will Rogers by the Will Rogers Memorial Commission and Oklahoma State University. It's available here. It is a compendium of the actual transcripts of many of his radio shows.