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It is difficult because you need to implement a USB host on the pic processor. Using compact flash with the pic is easier (the filesystem is a bit of an issue since it will need 512 byte clusters to work with a pc). You could then use a usb compact flash reader to download the data from the flash. You could also construct your system such that it acts as a usb peripheral and then you can use whatever type of storage you want.
Why not just save the data into an EEPROM and then send it serially? Unless you are looking at very long flight time you should be able to record it and once its back "download" the data to the PC thru the serial port.
I just saw a program in the Discovery Channel about model rockets and a competition it took place here in Kansas, US, that was pretty cool stuff..... what is a Hybrid Rocket?