Echoing others. Chickens don't have receptors for capsaicin, which is what makes hot peppers hot. They simply can't taste it.
The amounts one must add to the feed to have reliable and predictable effects and an antimicrobial is relatively high - not teaspoons per bag but more like 2% by weight, at which point it is:
A) not cost effective
B) displacing things of actual nutritional value
C) having statistically significant effects, briefly, on some microbes at rates which are measurable, yes, but not necesarily EFFECTIVE. Against certain e coli, its pretty effective as a control, reducing populations by about 75% - but not an effective treatment. against enteria, lactobacilli others the effect is 25-30% - possibly helpful, certainly not a cure.
It does, however, help tint eggs more orange, which the ignorant often mistake for sign of superior nutritional value (same reason some feeds include marigold).
Similar analysis for the antimicrobial values of various allium, thyme, oregano, others. Only in the case of alliums, the hemolytic properties run real risk of inducing anemia via red blood cell destruction.
and GOOD LUCK getting your birds to eat it. I have oregano, thyme, onions, scallions, and sometimes garlic in my garden. You know what my birds won't eat??? Thyme, Oregano, Garlic, Onions, Scallions. (they will sometimes eat a bug off an oregano leaf, and consume a bit of incidental greenery - but not in quantity sufficient to any dietary effect)