The Food and Drug Administration likely has nutritional information such as calories, sugars, fat and protein on many foods. The American Medical Association (Cardiovascular, American Diabetes Association, AAFP, etc.) could provide additional guidelines as well on nutritional information.
Current free and paid apps make the user the product by gathering users logged diet and unique identifiers. A government sponsored/provided open source app would respect user privacy, allows for citizens to contribute, and puts gathered data to real use.
With the success of the free and open source FCC Speed Test app available for both Android and IOS devices as part of the Measuring Broadband America program, it makes sense that other aggregated data could serve practical use.