You didn't mention which debugger you're using, but the same principles apply. The K16 sector size is 1 KB. A sector is typically the smallest programmable/erasable block of memory. In order to get this to work, you need to redefine the flash memory into two flash blocks. It sounds like you've already done this.
The memory range of the first block is now 0x00000000-0x00007FFF. The memory range of the second block is 0x00008000-0x0000FFFF.
You have to ensure the flash operation does not use mass erase. Most debuggers (e.g. MCUXpresso) allow you to erase by sector.
Thanks and regards,
MCUXpresso Support
EDIT: Sorry, you said 2 KB persistent storage. In this case, the memory range of the first flash block is 0x00000000-0x0000F7FF, and the second is 0x0000F800-0x0000FFFF.