If you've implemented mass storage class firmware on FX3 then you'll be able to send files by connecting to Windows mass storage driver. You can look at our FX2LP based NX2LP-Flex kit to get a better understanding of what I'm talking about http://www.cypress.com/?id=196
Even if you don't implement mass storage class you can send files using CyUSB3.sys. But in this case you'll have to implement your own custom protocol so that what is sent on one side is understandable on the other side. Especially if you're storing it in a storage of some kind it has to be stored in a file system format which means you'll have write code to take care of that part as well (will be a crazy idea).