DALLAS, Dec. 31— Ricky Nelson, who gained childhood fame on his parents' radio and television programs and went on to became one of rock-and-roll's earliest teen-age idols, was killed today along with his fiancee and five other people when his DC-3 plane crashed in flames near De Kalb, Tex.

The pilot and copilot survived the crash, but were critically burned, according to Michael L. Cox, a spokesman for the Texas Department of Public Safety in Austin.

Mr. Nelson, 45 years old, and the other victims were flying to Dallas aboard Mr. Nelson's plane for a New Year's Eve concert at the Park Suite Hotel in Dallas. The plane crashed in a wooded area near De Kalb, about 35 miles west of Texarkana.

Mr. Cox said the plane was on a flight from Guntersville, Ala., where Mr. Nelson's band had played a concert the night before. It was seen circling De Kalb erratically shortly after 5 P.M. and a Texas Department of Public Safety helicopter was sent up to ask if the pilot needed assistance.

The helicopter pilot was told there was a fire on board. The pilot of the plane said the cockpit was full of smoke and he was looking for a place to land. Plane Exploded on Impact

''The plane made one more circle over the area and then crashed in flames,'' Mr. Cox said. As it went down the plane also hit a power line and exploded on impact.

The survivors were identified as Ken Ferguson and Brad Rank.

The plane was so hot from the fire that rescue workers could not get close enough to recover the bodies of the victims, Mr. Cox said. He said the investigating officers discovered Mr. Nelson's identity because one of the survivors gave him a name to call and it turned out to be Mr. Nelson's manager. The manager confirmed that the plane was Mr. Nelson's from the registration number on the tail.

The survivors were taken to St. Michael Hospital in Texarkana, the Department of Public Safety spokesman said. A hospital spokesman said both were in critical condition with burns over the upper parts of their bodies. Plane Bound for Love Field

The plane was bound for Love Field in Dallas when it went down at 5:16 P.M. according to Mitch Barket, a Federal Aviation Admistration spokesman.

The other victims were identified by the Texas Department of Public Safety as Helen Blair, 27, Mr. Nelson's fiancee, Bobby Neal, 38, Patrick Woodward, 35, Rick Intzfield, 22, Andy Chappin, 30, and Clark Russell, 35. >---- Mr. Nelson was born Eric Hilliard Nelson May 8, 1940 in Teaneck, N.J., the younger son of Ozzie and Harriet Nelson.

When he was 8 years old, Mr. Nelson and his brother, David, first joined their parents' radio show, ''The Adventures of Ozzie and Harriet.'' It became a television show in 1952, and in 1955 Ozzie Nelson formed his own film company to produce it. The show continued until 1966, and is still being shown on some cable systems. A generation of television viewers watched Ricky and David grow up on the show. Ozzie Nelson died of cancer in 1975 at the age of 68.

In the late 1950's Ricky began to sing on the television show, and when he was 16 he recorded ''I'm Walkin', '' a Fats Domino hit, and became an instant idol of the teenie-bopper set.

After the television show ran its course, Ricky Nelson devoted his time to singing, and over the years he recorded scores of singles and albums.

He also made several movies, including ''Rio Bravo'' with John Wayne and ''The Wackiest Ship in the Army'' with Jack Lemmon.

Among his biggest record hits in the heydey of his teen-idol days were ''It's Late'' ''Lonesome Town,'' ''I'm Walkin' '' and ''Mary Lou.'' In later years he and his Stone Canyon Band helped lay the foundations of the Los Angeles country-rock sound that became prevalent in the 1970's.

Mr. Nelson was divorced from Kristin Harmon, with whom he had four children.