Hi Xavier
You can also try utFAT - http://www.utasker.com/docs/uTasker/uTasker_utFAT.PDF
This has more features that FatFS, including data caching between shared files, file analysis functions, undelete, as well as FAT emulation - http://www.utasker.com/docs/uTasker/uTaskerEmulatedFAT.pdf
Works with all Kinetis parts (with SPI or SDHC) and all common IDEs (IAR, Keil, KDS, CW, Atollic, Green Hills, Rowley, CooCox, etc.) and allows SDHC/SD card simulation in VisualStudio.
http://www.utasker.com/forum/index.php?topic=1667.0
Supports multiple disks (SD card, Memory Sticks, multiple USB-MSD LUMs).
Regards
Mark