Which of the following diseases is NOT commonly transmitted by flies?

Measles is primarily a viral disease that spreads from person to person through respiratory droplets. It is not transmitted by flies or other insects. The other diseases listed—typhoid, dysentery, and foodborne gastroenteritis—are associated with contaminated food or water and are often aggravated by the presence of flies, which can act as mechanical vectors by carrying pathogens from fecal matter to food sources.

In contrast, flies can spread bacteria that cause typhoid and dysentery, and they can also be linked to foodborne gastroenteritis by landing on and contaminating food. Therefore, measles is distinctly different in its mode of transmission, reinforcing its classification as the disease that does not commonly relate to fly transmission.