Solutions for implementing a USB Mass Storage Device
Lookup forebrain code examples, they use NXP LPC1343 chip that has USB mass storage drivers in ROM (so you can program the chip via drag and drop). Forebrain have example where they use internal ROM driver to present an EEPROM chip or simply just piece of RAM as mass storage device. They are closed source, but this gives the idea of how it could be implemented.

In general, you have to implement specific USB mass storage driver hooks. 

There is no need to make config file in any special format as you could implement FAT system on your chip so it accesses flash memory as FAT filesystem. You can lookup any SD card reading/writing example for popular microcontrollers - some use low level, some implement FAT. Particulary - this one for LPC1343 implements FAT over SD card: https://github.com/Miceuz/LPC1343CodeBase/tree/master/drivers/fatfs

BTW, have you considered an option to put configuration into a file on SD card? You would have loads of ready made code and examples for broad range of MCUs for that. Config process would involve extracting SD card from device and putting it into computer though.