No joke my high school principal's family is from Kansas and they made a chili for our competition. It was warm water with hamburger, beans, and tomato sauce. They got 3rd place.
I'm not an expert on Superman's super mouth and GI tract, but I have some thoughts.
First, whatever amount of spice that would approach Superman's limit would be intense enough that mere humans couldn't be anywhere near the chili cooking. The amount of capsaicin in the environment surrounding the chili pot would be toxic and possibly fatal.
If he was making the chili at the Justice League headquarters the following would happen when Superman offered the chili to the others:
Flash would phase around the capsaicin molocules and say that it was really great in a very non convincing way.
Wonder Woman would take a bite and with flushed cheeks mention that the Amazonian women made a chowder that was a little hotter.
Martian Manhunter would take a whiff of the Chili and decide that the sensation was too close to burning for his liking.
Plastic-Man would be so annoying with his antics following a taste that Superman wouldn't offer him any even though Plastic Man would be fine eating it.
DCEU Aquaman would take a bite, and though it would burn and cause him hours of misery, he wouldn't show it and proceed to drink 2 cases of beer.
Batman would enter the kitchen in his Bat-Hazmat Suit and direct Clark's attention to the posted rules for appropriate workplace food and mention that he expected everything to be cleaned up before the end of the workday. He'd then extract a sample of the chili for analysis and formulate countermeasures in case it was ever weaponized.
Green Lantern would will himself to eat a bite, but surreptitiously surround the bite with a force bubble so his body didn't have to actually ingest it.
Depends. He is indestructible and, as far as I know, not a renowned chef. Cooking with ingredients that you actually put in food should be totally safe for him.
He might be able to find some kind of exotic alien substance that could cause some physical pain, but at that point, is he really cooking? Or just adding something painful to food?
Sidenote, he could probably find some kind of kryptonite that would disable his powers for a meal.
I don't see how any of superman's powers would improve his ability to cook spicy food, so no.
If he were said to be omnipotent, this would be an interesting conundrum. But he isn't so it doesn't really work?