The time it takes for a person to get sick from eating bad chicken depends on how much bad chicken you ate and how bad the chicken was.
Some people may get sick after 2 or 5 hours of eating the bad chicken then somebody else may not get sick until 24 to 48 hours later after eating the bad chicken.
Most people though will start feeling bad within a few hours to 10 hours after eating the bad chicken and usually it's nothing to worry about.
Most times the illness from eating bad chicken will pass within a day or two and you'll usually have a stomach ache and vomiting and probably diarrhea.
If you're still ill after a few days then going to urgent care or the emergency room would be a good idea to make sure you're not more severely ill.
When chicken has gone bad you'll usually see a change in the color of the chicken and it will taste bad or even have a bad smell to it.
Chicken though as long as it's remained frozen or refrigerated can last from 6 months to a year in the freezer and around 5 days in the refrigerator for cooked chicken.
Raw chicken could last for a few days in the refrigerator and any longer than that you should freeze the raw chicken.