They don't need scheduled vet care. But eventually you will end up with a sick or injured bird and you'll need to make a decision. Most people (understandably) won't take sick/injured chickens to the vet, and if you are new at this, it can be an especially difficult decision.
I am in the minority, I do take my girls to the vet when they are sick. I luckily found a vet who charges me very little to take care of the chickens, he has taught me to tube feed sick birds, administer injections, and he's given me homeopathic remedies. For example, my one-legged chicken (Special Edna) sometimes has a sore leg. Not good for a one legged chicken. We've been giving her fish oil for it, which is a natural anti inflammatory, and it works! . This vet is a very rare find.
Best bet is to learn as much as you can about taking care of sick birds on your own; make friends with others who have this kind of knowledge who can help you; make contacts with a vet who takes care of farm animals - they charge less and will allow you to treat the animals yourself more than a companion animal vet, saving even more money. Get your chickens used to being handled so you can find problems early; read about how to spot problems early to avoid bigger problems later. And get mentally prepared for the day when you have to decide between spending $$$ or letting (or helping) a chicken die.
Good luck
Colleen