Raw NOR and NAND flash memory is handled by the Memory Technology Device subsystem, or MTD, which provides basic interfaces to read, erase, and write blocks of flash memory. In the case of NAND flash, there are also functions to handle the OOB area and to identify bad blocks.
For managed flash, you need drivers to handle the particular hardware interface. MMC/SD cards and eMMC use the mmcblk driver; CompactFlash and hard drives use the SCSI disk driver, sd. USB flash drives use the usb_storage driver together with the sd driver.