I assume you mean a 'USB' FLASH Drive. In that case you'll need a uP that acts as either a USB Host or OTG. Microchip has an application note that deals with that (AN1145) at:
**broken link removed**
go to Microchip website and search for: "Microchip USB framework", there are many ready made projects for implementing USB mass storage drive using PIC microcontroller on various hardware platforms starting from PIC18F4550 to PIC32.