1- Make your "Sketchbook location" point to a subfolder in Arduino IDE like D:\Dropbox\Arduino
2- Make a hardware subfolder in it like D:\Dropbox\Arduino\hardware
3- Put the esp8266com folder from https://github.com/sandeepmistry/esp8266-Arduino repository in this hardware folder like D:\Dropbox\Arduino\hardware\esp8266com
4- Launch/ReLaunch Arduino IDE
Repeat steps 1 and 4 in other machines with the same Dropbox account.
That's it.