Throughout The Flintstone's original six-year run...and its many, many reboots, spin-offs, and specials...they never give a definitive answer as to what Barney's profession is. Early on, in the series black-and-white days, they elude to him being a 'short-order cook', a job that he frequently gets fired from. The show was roughly modeled after The Honeymooners, and Barney quite literally being the Ed Norton to Fred's Ralph Kramden.
In a later spin-off, Barney can be seen working alongside Fred at Slate Rock and Gravel Company, but beyond that, you only get a few vague snippets as to what he does for a living. Among them are: a private detective, photographer, custodial engineer, Fred's boss at the quarry, a (television) repossession agent, geological engineer, and substitute teacher.
So, to see him as a Geology 'teacher' isn't that much of a stretch
See Barney and his 'star pupil' at the $1 tier level. :D
Original Art by Alex Hiro
Colors and Edits by Phillipthe2