Many eprom burners can write eeproms and flash. I know mine can. For developement, why not use a micro with the flash internal and ISP as they normally don't require a eprom burner to load the code.
I second the use ISP statement.
re burning the EEPROM in an EPROM burner the answer is simple: If the chip is in the devicelist it can, if not, it can't

Erik