It depends on the size of your flock and your commitment to them. Personally, I don't feel like they take up a lot of my time, but I enjoy spending my time with them. An established backyard flock doesn't usually require a ton of work.
I spend about 20 minutes a day doing necessary chores (filling up feeders, refreshing water, collecting eggs). This takes about 40 minutes in the summer, as there are extra things I have to do here in AZ to keep them from overheating. I clean the coop once a week, which usually takes me about 2 hours by myself (I have three pens to clean). During this time I also do health maintenance (checking for external parasites, making sure their droppings are normal, trimming nails/feathers if needed). Where I live, I can't let them free range without supervision, so I do spend a good chunk of my free time outside with them while they forage (they have a big enough coop where this isn't necessary, just a nice bonus for them).
But a big part of chicken care is spending time with them and observing them. It's important to understand the hierarchy of the flock and the 'normal' for each bird. It then becomes much easier to realize if something is off. I also get a lot of joy out of spending time with my birds, so I spend more time with them then is technically needed. Then again, why have pets that you don't enjoy to some level?
However, all of this will vary based on your situation. Flock size, coop size, flock age, flock health, their purpose (breeding, eggs, meat, enjoyment), and much more will all change how much time you spend taking care of them. From time to time, chickens will get sick or old. It's just part of keeping them. Sick birds will require much more maintenance and time. Baby chicks also take up a little more time, and the time you spend with babies will have a direct correlation to how friendly they will be as adults. When you introduce birds, you will need to check on them much more often to make sure no one is fighting.
Every situation and every flock is a little different. But that's the advantage of having communities like this, so you can ask questions and check-in anytime you need.