Should I drink a lot more water if I am having a flu?

Yes. Fevers increase energy consumption and your body needs extra fluids.
Yes. The fever and less appetite from a flu-like illness can quickly lead to dehydration- which can be very serious. More hydration with plain water in beginning will be better for sure!

Related Questions

If I feel a flu coming on, is there anything preventative I can do to stave it off? Do drinking water and taking vit C actually help?

Flu. Staying hydrated and eating healthy is best. Vitamin helps with your immune system, which can help battle the flu. If it is confirmed with a swab you can take tamiflu (oseltamivir) to help with symptoms. Hope this helps.
Yes. Rest and hydration are key and eating healthy foods can help sometimes and if nothing else should shorten the duration of your illness.