If the milk comes out of the mouth, the hole is too big and you need to replace the nipple with one with a smaller opening. Kittens should start drinking water on their own at 4-5 weeks of age. Don't get frustrated when they are only playing or walking in it. One day, you will see them drinking. There are some home made remidies which work, too.
Most grocery stores carry goats milk, and it is available in condensed form to keep in the cupboard.
Available from a pet store, your vet or a feed store. KMR is available in both mixed and dry version. The dry is more economical. There is a trick to mixing the water. Get a small container with a secure lid.