I am using SSP0 on the LPC4088 with SSP_FRAMEFORMAT_SPI and experiencing similar issues.
It appears the LPC4088 shifts a frame in/out of the FIFO whenever the chip select goes from the low state to the high state.
I believe for SPI communication the chip select is normally held low for the duration of a transaction (multiple frames) but for some reason the LPC4088 instead uses the chip select to indicate the transmission of a single frame.
I am using a Linux device as the master and ioctl to send SPI messages, looks like I might have to set up a new transmission for every frame.
Also, the interrupts offered by the SSP are not useful if I want to load a new transmission frame based on a received frame, normally for SPI peripherals you would expect to have an interrupt when a new frame has been received but the interrupts for the SSP lack this. Looks like I will instead have to use a GPIO interrupt on the chip select line (a long with the chip select line being toggled between every frame) to load the next transmission frame into the FIFO.