Born in La Grande, Oregon, McKennon's best-known roles were that of Gumby for Art Clokey, and Archie Andrews for Filmation's Archie series, and the primary voice of Buzz Buzzard in the Woody Woodpecker cartoons. In the early 1950s, McKennon created and hosted his own daily kids TV wraparound show, Space Funnies/Capt. Jet, which was seen weekday mornings on KNXT (KCBS) TV Ch. 2 in Hollywood, California. Space Funnies was the first Los Angeles-based kids show to air reruns of The Little Rascals and Laurel & Hardy Film Comedies. He was also the primary voice actor for the 1960 cartoon series Q.T. Hush. McKennon was also the voice of Hardy Boys sidekick Chet Morton in the 1969 animated mystery series.
McKennon also sang, and provided many character voices for Disney. His distinctive voice can be heard in movies such as Lady and the Tramp, Sleeping Beauty, One Hundred and One Dalmatians, Mary Poppins, and Bedknobs and Broomsticks. He also provided the voices for many Disney Attractions such as the famous Big Thunder Mountain Railroad safety spiel, Ben Franklin's voice in Epcot's The American Adventure and the voice of Zeke in the Country Bear Jamboree.
McKennon's best-known live action role is that of the innkeeper, Cincinnatus, in the Daniel Boone TV series starring Fess Parker. He also had a bit part as a chef in the Alfred Hitchcock film The Birds and a gas station attendant in the Elvis Presley film Clambake. His last movie was Gumby: The Movie, under the pseudonym of Charles Farrington, voicing Gumby, Fatbuckle, Lucky Claybert and Professor Kapp.
McKennon was an avid Oregon Trail historian. He worked at the Oregon Trail Interpretive Center giving instructional speeches. He also put together songs, stories and informational documents leading up the Oregon Trail's sesquicentennial (150th anniversary).
Dallas also worked with OPB (Oregon Public Broadcasting) creating "The Pappenheimers", an instructional video series to help teach children German. His character lived in Volkswagen Bus and would tell stories about relatives in Germany. Many of the episodes had clips of Germany as well as cartoons.
McKennon married childhood sweetheart Betty in 1942, a marriage lasting until his death. The couple had a total of six daughters and two sons. He was also a devout born-again Christian.