I was under the impression that flash memory was another type of EEPROM.
Technically, flash rom is another type of "electrically erasable" rom, but this doesn't tell us how it can or can't be used in practice 
Flash ROM is where the program code is stored. EEPROM is the user-accessible one. So basically yes, you just have 1KB to store data. To increase that you have to go the sd route or add an external (i2c ?) eeprom chip.