Valid question and one that is raised very often. First off, ALL laying hens and dairy cows are slaughtered for their flesh. Let's start with chickens. An egg may not be conscious, but the hen is. It is a product of its body. Laying hens are forced to live their lives confined in cages, never to see natural light, some have their beaks seared off with a hot blade and they are bred to lay unnaturally high numbers of eggs (~300 per year; wild hens lay ~15 eggs per year). They often suffer from prolapses and the intensification of this breeding is incredibly taxing on their bodies. So, egg production and consumption is inextricably linked to chicken slaughter. Same with cows. Milk isn't sentient, but the mother cow is. Dairy cows are continuously artificially inseminated, so that they get pregnant and start producing milk. Once the calf is born, it is taken away within hours or days and the mother cow is then put into the intense milking process. The bobby calfs are then taken to small pens and chained by the neck, to the point where they can hardly move. This is done to prevent muscle growth and hardening, so that the infant can then be slaughtered later for veal. Once the dairy cow is 'spent', she gets sent to slaughter. Cows have a natural lifespan of ~20 years. A dairy cow can go for between 4 and 6 years before her body gives in, milk production falls and she's not economically viable anymore. So, milk production and consumption is inextricably linked to brutal exploitation and slaughter. Now, about your backyard chicken. If you bought got the chicken from an industrial hatchery, she'll be laying a very high number of eggs. It would be better for you to feed the eggs back to her, allowing her to replenish lost nutrients, vitamins and so on. If you have a cow, if she is not pregnant, she will not produce milk. If she has a calf, the calf will drink from her.
