I give it once a month - for a week, I do it in the first week of every month so I don't forget, this is after I have built their resistance up. My chooks do free range though and I would probably increase this if they were more enclosed.
As cyberchicks said, it should not be a replacement for a wormer - but yes, it is supposed to increase the acidity in the gut which makes life more uncomfortable for worms - I'm not so sure about Gape Worm though that is found in the crop.
Can you be sure they died of Gape Worm?
Here's a little more information about Apple Cider Vinegar and Chickens
it does need improving a little but ACV seems to be one of those things that people say gives them fantastic results but finding hard facts about it is a little more difficult since there always so many variables involved!