You can manually add the FastLED library to the arduino libraries by adding the FastLED code files to C:\Program Files (x86)\Arduino\libraries\FastLED. (C:\Program Files\Arduino\libraries\FastLED on 32 bit). I can't remember the library path on linux, but I can get it for you if you need it.
You can get the FastLED library from here:
https://github.com/FastLED/FastLED. However, it seems like you already have it, so just move the code files the path listed above. You will need to create the FastLED folder inside libraries folder and paste all the code files directly into FastLED folder.
After that, you can change the include to #include "FastLED.h".
I was able to compile after doing those two things.