The modern flu is fought through maintaining a stress free environment, bed rest aka inactivity, and keeping yourself clean, aka preventing secondary infections from overwhelming an already occupied/compromised immune system. Secondary infections cause the immune system to divide it's attention. Stress, a mental component, has a high psychosomatic component, resulting in a handicapped immune response. Mind over matter, essentially the placebo effect, is real. Activity wears down body resources, like glucose levels, which are crucial to fighting infections. A tired, afraid person will take longer to fight an infection then someone well rested and calm. It's not just that it's the flu, but the entirety of the circumstances that increases the death toll.
Remember, everyone in the Walking dead is already infected with the Zombie virus. As long as they die with their heads intact they will reanimate. As such, the immune system is already dealing with more than one infection at the time they get the flu. Immuocompromised