The FL256L is default in SPI mode, if you want to use the Quad-SPI mode, you should config the CR1V (config for every power on) or CR1NV (config only for 1 time) to enable the Quad-SPI mode.
Please refer the section 6.6.3 of the datasheet for more information:
Customer Application Engineer, Cypress
Thank you so much. You're right, the flash must be configured to QUAD mode (WRR to CR1NV). Not only it enables quad write in page, most importantly it enables Xilinx FPGA to load configuration in SPIx4 mode at power up.