It's NOT distilled vinegar - it is organic apple cider vinegar. You may put a little organic apple cider vinegar in their drinking water (will find in a health food store or online). Not sure of the quantities - sounds like a 1 tsp is too small to do much good for a gallon of water - but I know it does not hurt the bird at all.
You may use distilled vinegar mixed in water to clean cages and perches. But I haven't heard of anyone using that for drinking water.
Alternative is to put a drop of GSE in the water dish. Here's a link with info:
Winged Wisdom Pet Bird Magazine - Kitchen Physician VII - Citricidal: Cure & Disinfectant For Parrots and Pet Birds