It's more convvenient to have one syringe per chicken, I grant you, but if you have a helper, you can do it with only a few. I wouldn't depend on just one; after several uses, they will come apart; they are designed only for one use, of course.
To get the air out, hold the syringe with the needle end up, pull the plunger back a little then flick the syringe, tap it with a fingernail, til the air floats to the top, then push it out carefully. If you are drawing out of an injectable bottle, push into the bottle about the same amount of air that you will be removing in medicine.
I bought one syringe and two needles from my feed store for 25 cents. However, they didn't carry 1 cc size. If I wanted 20 or 30 of the 1 cc size, I'd go to my vet and tell him what they were for, and insist on paying cost, which would probably be a very few bucks. (I was using ivermectin injectable so 3cc worked OK for me.)