It is claimed that eating coconut cream or using the oil helps, especially during the early stage when you are "sickening" for the disease.
This is because coconut oil contains lauric acid, which is turned to monolaurin in the body, and this is said to dissolve the cell walls of lipid-coated viruses. The 'flu virus is lipid-coated, as are the measles virus and HIV. In fact, before effective drugs were developed, many people with HIV would use a porridge made from coconut to keep down the viral load.
Monolaurin, however, cannot cross your own cell walls, and so is only effective in the inter-cellular spaces. What this means is that it does not eliminate the virus from the body completely but is effective in limiting its ability to multiply. Since it takes the body 3-4 days to produce antibodies to any new antigen, the virus tends to run wild during that period. Taking substances like monolaurin during that period therefore reduces this and makes the job of fighting the disease more manageable for the immune system. It can still help to take it later, but at that early stage it can be the most effective.
If you find yourself with those first signs, it might be a good idea to make yourself some coconut ice-cream, shake or smoothie, or even make a pina colada, or a Thai curry, if you can't eat coconut cream straight. If you really hate it, you can buy monolaurin in supplement form. Don't buy the reduced fat kind of coconut cream, as the lauric acid is in the fat.
Apart from its effect on lipid-coated viruses, it is said to have anti-bacterial, anti-fungal and anti-protozoan effects, and to be useful against helicobacter pylori, listeria and giardia. If you're interested in the scientific explanations, Doctor Mary Enig has written a lot about the benefits of coconut oil and Dr Harry Preus has published his research on them.
Another hint I have been given is that if your first sign of 'flu is usually a sore throat or swollen tonsils, slowly sip some aloe vera juice (maybe a tablespoonful) and let it trickle over the sore area, as this is anti-viral. I can't verify that this works as I haven't read any research, but I guess it can't do any harm to try it.