Hi, K.! :)
I had this same problem. It's really common. The little babies just need time to adjust to this new thing. People just have to have the patience to be consistent with it. But a lot of us try to rush the child by adding sugary items in with the milk. DON'T DO THIS. Especially not NesQuik. There's just too much sugar in there, especially for a 13 months old baby.
I tried everything - she refused to drink her milk and I was so scared that she would get dehydrated, so I gave her juice instead. What I didn't know is that you're not supposed to give children more than 4oz of juice a day (because of the sugar). Thank God, I found this out just 2-3 weeks after I started giving her bottles of juice to keep her hydrated.
In the end, I found out it was the sippy cup she didn't like. I started her out on the Avent sippy cups. She HATED those. *I* hated those. They leaked like crazy.
Then I tried the NUK sippy cups because the spout was more like a bottle nipple. She liked those better, and they were fine for several weeks, but she still didn't drink nearly as much as she needed, AND they still leaked just a bit.
Finally, I tried the Playtex sippy cups. The ones with the handles built into the lids. They come in green/blue, purple/yellow, pink/lavender, red/blue, etc. You always seem them in the baby section of grocery stores, as well as at baby stores.
My daughter GLOMMED onto these. I highly recommend them. They have a sucking mechanism similar to a bottle and then you can take the clear rubbery thing out so that when they get older, they can drink without sucking and transition to a regular cup. They are great for teething (my daughter loved to chew on them sometimes) and they don't leak.
If you are desperate, however, and must mix something into your child's milk, make it something like 1 oz vanilla-flavored soy milk, added at the very top of the milk. Something like that won't give them a sugar-rush/overload.
But if you don't wanna do that, you may just have to start at 1/3, and after a week or two, go to 1/4 and then after a week or two, phase it out more and more, little by little, until he doesn't even know he's got all milk.
I hope that helps!