The SDK is linked into every Arduino application you flash to the ESP8266 - it's not flashed separately.
Presumably you've already followed the instructions to put the URL for the ESP8266 Arduino Core in the preferences for the Arduino IDE.
Once that's there, to update the ESP8266 Arduino SDK, go to the Tools menu, select Board, then select the Boards manager (the first item in the menu).
That will bring up a dialog listing all the board families your Arduino IDE knows how to build for. You can limit the list to those with updates available by selecting "Updatable" in the "Type" field. Or just scroll down or search till you find the ESP8266 entry. Click it and if there's an update available you'll see an "Update" button appear on it. You can also reinstall older versions by choosing a version and clicking the "Install" button.
However, there is no version 3 as yet. At the time that I'm writing this, 2.5.2 is the most recent release of the SDK.