I'm struggling with LPC55S69 flash issues today myself. The first thing to check is your clock source - it won't work properly with a clock above 100 MHz.
There are references in the MCUXpresso SDK code that make it look like it's specifically expecting to be run from the FRO96 clock source. I don't think it's true that that's the only source you can use, but it's what all of the examples use, and if you check FLASH_Init() you see this as the first line:
/* Initialize the clock to 96MHz */
config->modeConfig.sysFreqInMHz = (uint32_t)kSysToFlashFreq_defaultInMHz;
And here kSysToFlashFreq_defaultInMHz = 96u so the driver seems to expect that to be the only configuration. The documentation is terribly inadequate so who knows what it's actually capable of. I'm writing a bootloader today and I'm just going to assume that the FRO96 is the only valid clock source. Thankfully the bootloader doesn't need to handle any other interfaces or anything with critical timing.
Scott