As far as I can tell ....
ESP8266WiFi.h <-- WiFiClient.h <-- Stdint.h <-- Interrupts.h <-- ets_sys.h <-- eagle_soc.h
I hooked up CTS and RTS the standard way ...
Microprocessor RTS (Output/Driver) -----> 8266 CTS (input) (GPIO13)
Microprocessor CTS (Input) <----- 8266 RTS (Output) (GPIO15)
The signals are active low, i.e. when they are low the 8266 UART sends/receives normally. But this can be inverted in the 8266. BTW, I'm using a ESP8266Mod, but that shouldn't make a different.
Hope this helps.