I suspect it's a combination of advertising and marketing materials (e.g., educational videos, comic books), many produced by the oil industry itself, which promoted the meme.
Sinclair Oil's mascot, dating to 1932, was a factor. I looked through Google Books with some date-ranged searches for "dinosaur" and "oil" or "petroleum". That excludes the video and comic-book evidence, but what seems to show up, even in congressional testimony, are references (mostly tongue-in-cheek) beginning in the 1970s. Given the archive's limited scope, I suspect that the concept could have been picking up in the 1960s or 1950s. Note that this corresponds largely with the widespread adoption of television, which goes in hand with simplified and infantalised messaging through both advertising and mainstream programming.
But the notion was definitely "in the air" as of the early 1970s.
Airplane II was released (or escaped) in 1982.