Well, yes, milk can be helpful to treat burning eyes. Generally speaking, milk is used in many ways, but we can also use it to protect our eyes, especially when someone suffers burning eyes. In my opinion, you can just get a soft cloth with cool milk, and then put the cloth under your eyes. In that way, it will be effective. Also, you can have some cold compresses, and put some cool ice or cool cucumbers on your eyes. In that way, it can relieve your symptom and make you feel well. Also, you should eat a diet rich in fresh fruits and vegetables which provide lots of antioxidants, especially vitamins A and C and then do a good job to your symptom. Anyway, just have a try.