We had the same situation (where our son needed the extra nutrition), we had the doctor write a note and had added to his 504 plan. The school is required to provide accommodations like this…that is what a 504 plan is for as malnutrition is a major contributor to school performance.
If you need options…we use the Boost High Protein (with 20g of protein per drink). While it has 15g of sugar, he loves the taste and we know he will drink it. Our son actually drinks it in class, right after recess in the afternoon. That way it supplements what he may eat for lunch vs. replaces it. We needed a high protein drink that my son would actually like, as we have a difficult time ensuring he has enough protein because of his texture issues so this one fits our needs. These are much cheaper ordering on Walmart.com versus getting at the grocery store. FYI – Boost also has a lower sugar one (16g protein, 4g sugar – glucose control), which may be an option but we haven’t tried that yet as it is way more expensive.
Good luck!!! I know what a worry your son not eating can be, so my prayers are with you.