There has been much conjecture over the meaning of "Jimmy Crack Corn and I don't care." However, in the oldest version it is "jim crack corn", and "jim crack" has always meant something cheap or shoddily built, and "corn" is an American euphemism for "corn whiskey".
From a petroleum engineer's perspective, this could simply refer to corn whiskey. "Cracking" is, in general, a process of reducing an input substance to a desired output substance ... so "cracked" corn might be corn whiskey. "Jim" could be a generic reference to the person owning the still; much as we refer to the generic "John Doe" these days.
One possibility is "gimcrack corn," cheap corn whiskey; another related theory is that it refers to "cracking" open a jug of corn whisky; another is that "crack-corn" is related to the (still-current) slang "cracker" for a rural Southern white. Another interpretation is that "crack corn" came from the old English term "crack," meaning gossip, and that "cracking corn" was a traditional Shenandoah expression for "sitting around chitchatting." Yet another, and possibly the most popular, is that the chorus refers to an overseer who, without the master, has only his bullwhip to keep the slaves in line. Most etymologists support the first interpretation, as the term "cracker" appears to predate "corncracking", and "whipcracker" has no historical backing. This suggests that the chorus means the slaves are making whiskey and celebrating.
https://en.wikipedia.org/wiki/Blue_Tail_Fly