It really depends on the Flash programmer. Fundamentally, Flash and EEPROM are separate peripherals with different programming interfaces. Actions performed to one will have no effect on the other.
LPCScrypt can be used to program and erase EEPROM and also supports an erase all command - this simply calls the erase function of all programmable devices known to LPCScrypt on a particular MCU.
Also LPCOpen provides example code to manage the programming of EEPROMs.
Yours,
LPCXpresso-support