What I know from accidental experience about chickens and changing the taste of eggs by what you feed them.
Disclaimer: Chili isn't really that good for them. Didn't harm them, but it didn't do anything much for them.
Eating weird, spicy or strongly flavored food won't change the eggs, at least from what I experienced.
My flock of hens loved to sneak into my compost piles at the old farm and help themselves. My late father Loved chili.
And by loved I mean he'd have eaten it morning, noon, and night if I'd have let him. All leftovers ended up in the compost and thus in the chickens. Never had any chili flavored eggs. Or hot pepper flavored either.