If the green light around the power button in the Xbox 360 flashes green, it could be because the batteries in the controller are going to die. Therefore, the green light around the power button in Xbox 360 controller will flash green, to alert you to replace the batteries before they die. To test if the batteries inserted into the Xbox 360 controller are dead, get a battery tester that is compatible with AA batteries and test if they are dead. If they are dead, replace them with brand new batteries and hopefully this problem will be resolved.
If the batteries are not dead and if the Xbox 360 controller is wireless, not wired, it may need reconnecting to the Xbox 360 console. This is by powering on both the console, as well as the controller and press the button next to the memory card flap on the console and press the little button found at the top of the controller, near the charging socket. This will re-sync the controller with the console and resolve most flashing green light problems.