My flock usually runs between 50-100 head. I've raised chickens for more than thirty years and I provide excellent care and medical attention as needed; your results may vary.
We had a little family, mother and two of her chicks that lived to 14, 16, and 18. They were bantam mixes. I've also had others live to over ten, but it is pretty rare. Usually, chickens succumb to natural complications or minor illness between five and ten years.
My shortest lived chickens have been heavy breeds. I once tried to "save" two Cornish X roosters and both died of leg weakness and ascite by six months. I also have had some production reds who had a heart defect and all dropped dead by two, heartbreaking. I have had very good luck with long-lived Dominiques, silkies, Barred Rocks, and mixed breeds.
My egg production is best in the first two years, but hens continue to lay and ovulate throughout much of their lives, though less regularly. My 16-year-old hen laid an egg every couple of days, brooded her own clutches about twice a year, and died defending a brood of her own chicks from a coyote. You won't see her like very often. Most hens won't just stop laying as they age. They will slow down, respond to molting, weather, seasons, illness, and food availability, but with excellent care they will continue to lay well into old age.
My best tips for stimulating egg production in hens young and old are high protein foods and supervised free ranging for plenty of bugs and greens.