Hi unknowncoder,
Thank you for your interest in NXP kinetis product, I would like to provide service for you.
Answer your several questions:
1. What is the maximum storage capacity of the EEPROM subsystem? As far as I understand it's the size of the FlexNVM which is 256KB.
The maximum storage capacity of the eeprom is just the flexRAM size, it is 4KB, FlexNVM is just the eeprom backup memory, you don't need to care about it.
Actually, the reference manual also mentioned it:

2. Is there an easy access API to using the EEPROM
At first, you need to do the eeprom partition, then you can do the eeprom write and read operation, If you want to write the eeprom, you just need to use the FLEXNVM_EepromWrite().
About the EEPROM read, that's very easy, the eeprom address it he flexRAM address, you just need to read that address data is OK.
Take an example:
#define LONGWORD_COUNTER_ADDR 0x14000040
#define WORD_COUNTER_ADDR 0x14000044
#define BYTE_COUNTER_ADDR 0x14000046
printf("\nlongword counter = 0x%08X", *(uint32 *)(LONGWORD_COUNTER_ADDR));
printf("\nword counter = 0x%04X", *(uint16 *)(WORD_COUNTER_ADDR));
printf("\nbyte counter = 0x%02X", *(uint8 *)(BYTE_COUNTER_ADDR));
About the write, I also have the k series EEPROM register control code, please check the attached .c file.
3. When you write, you also need to give the flexRAM address which already simulated to the EEPROM function.
Wish it helps you!
If you still have question about it, please kindly let me know.
Have a great day,
Kerry
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