The most common reason that you lose your appetite with the flu is because you have a lower energy level.
When your energy is too low then you do not feel like eating because eating and digesting food requires energy from your body.
So when you're suffering from the flu and have low to no energy your body basically wants to reject the food even when you try to eat it.
However it's best to at least try to eat some chicken noodle soup which is easy to swallow and get down when you have the flu.
But even when you don't feel like eating at all it's okay to go a day or so without food as long as you're drinking plenty of water or some tea to stay hydrated.
Chicken noodle soup is also hydrating so you keep your fluids up and you get a little bit of food in your body.