SPI in vendor mode will expect the exact number of bytes of data specified in the length parameter of the read buffer (CY_DATA_BUFFER* readBuffer), else it will return with an error if the data received is more or less.
1. You can configure the length parameter of the read buffer to 255 and call the CySpiReadWrite repeatedly for n number of times , make sure that the delay is very less between the calls (or) you can set up the buffer length to 255*6.
2. You can also add a flow control. Set a gpio as input on the USB-Serial device and whenever the master wants to send data, it can notify the USB-Serial device through the gpio.
If the master continuously sends data, then you can try using the CY7C65215A (pin compatible with CY7C65215) which has SPI in CDC mode. You can open a terminal like tera term to continuously capture the data or develop a custom host application using the USB-Serial VCP library.