Same thing on SCLK and MOSI, they should stay tristate otherwise will affect the other devices and (I suspect but I'm not sure on the ESP8266 the FLASH chip it's using the same SPI line).
A possible solution it's use a tristate buffer like 74HC125 followed by 74HC04 to invert SPI lines, the buffer should have all enable lines tied to CS so the whole device will be active only when CS is low then return high impedance and result imvisible to the other SPI devices.