No, not compatible with ESP8266 client. Got this error:
WARNING: library ThingSpeak claims to run on [avr] architecture(s) and may be incompatible with your current board which runs on [esp8266] architecture(s).
WeatherStationDemo.ino:33:33: warning: extra tokens at end of #include directive [enabled by default]
WeatherStationDemo.ino:34:34: warning: extra tokens at end of #include directive [enabled by default]
In file included from WeatherStationDemo.ino:36:0:
C:\Users\x\Documents\Arduino\libraries\ThingSpeak\src/ThingSpeak.h:81:8: error: #error Only Arduino Yun, Uno/Mega/Due with either Wired or wi-fi Ethernet shield, and Spark Core/Photon are supported.
#error Only Arduino Yun, Uno/Mega/Due with either Wired or wi-fi Ethernet shield, and Spark Core/Photon are supported.
^
C:\Users\x\Documents\Arduino\libraries\ThingSpeak\src/ThingSpeak.h: In member function ‘bool ThingSpeakClass::writeHTTPHeader(const char*)’:
C:\Users\x\Documents\Arduino\libraries\ThingSpeak\src/ThingSpeak.h:1357:28: error: ‘TS_USER_AGENT’ was not declared in this scope
if (!this->client->print(TS_USER_AGENT)) return false;
^
Error compiling.