While others may swear by it, I do not think new chicks are really set up for ACV.
When I have a sticky chick that won't fluff, I fill the sink with 100F water, have a soft small towel warming in the brooder, and have baby shampoo or blue Dawn on hand.
With the chick's head between your index and middle finger in your left hand, submerge the chick's body leaving the head well clear of the water and massage the body with your right hand. Lift it out and add just a couple drops of baby shampoo or Dawn to the chick's back, then massage gently all over the chick's body. Be VERY careful around the navel and vent. Dip to rinse, then wrap the chick in the towel. After a few moments, loosen the towel and allow the chick to wiggle around inside the towel. Then release under the brooder lamp.
After this first bath, only vent wipes should be necessary.