I'm going to get flamed for this.....but...
Your first priority should be that your hens are kept in clean surroundings with access to the outside and sunshine. They should not be overcrowded.
Clean fresh pasture, and open air is the best tonic for a healthy chicken.
Given this, all you need then is access to a healthy clean fresh water supply, and nutritious feed appropriate to their age, and supplements such as oyster shell calcium for laying hens.
If your water is always clean and fresh, then you won't need stuff like vinegar to help kill bacteria that poor hygiene has created.
Although garlic may be a natural antibiotic, if you raise your chickens right, you won't need to give "sub-theraputic" doses of antibiotic like the "big boys" do, because you have great animal husbandry, and healthy chickens.
Besides....garlic can create eggs with garlic flavor.
God bless you for wanting to do right by your chickens.
Just protect them from predators, and give them clean water, and the best feed you can afford, and plenty of space to be chckens.
That's truly the key! I have 800 chickens thriving on that recipe!
Good luck
Rachel, TX