I maybe late but here how it is done. Netlify should have special file in your root directory called __redirect and you can define your proxy there like

​

/api/* https://yourapi.domain.com/:splat 200

/* /index.html 200           

Then you can call your api like this

​

const res = fetch('/api/user')   //equivalent to https://yourapi.domain.com/user

Hope this helped