While the M7 does support OTG USB, you need to make sure that your cable is working and that the flash drive you're using doesn't need external power or too much power (regular USB Hard Drives will NOT work unless you supply power externally). Have you tried the cable in a different device?
Also, if your device recognizes the flash drive but can't read it, remember that it needs to be formatted as FAT32 or ExFAT for your Android device to be able to read/write to it.