I used to give my girls red pepper flakes (just tossed a handful out, not in the feed, but as if I was tossing out scratch), and they'd gobble it up like it was candy. They loved it (I've not bought it for a while), but I never saw any real difference in their winter egg laying. Mine (it's a breed thing) take off from Oct. to mid January. In fact, we're just starting to get some now. I don't put up lights, I don't like forcing them to lay like that. This coming spring we're getting new chicks from breeds that are known for winter laying. I may not get as much as someone using lights, but that doesn't bother me, as long as I get SOMETHING.
Be patient, the days are getting longer, and they ought to be starting up again soon. OH, the hot pepper flakes won't change the flavor of the eggs (that I noticed), but the chickens may love it, and it may aid in their health, so I see nothing wrong with feeding them the pepper flakes. Like I said, mine love it.
Ahhh tea the essence of life.