How to move dock items?
It's a smooth click and upward motion on an icon using your mouse or trackpad to rearrange icons in the Dock. Don't click-and-hold, click and move -- if you click and hold you'll get the option menu overlay for the application.

Tried to make a little gyfcat that shows it happening:

http://www.gfycat.com/ClearcutUnluckyAndeancondor

This irregardless of the setting for Keep in Dock on the application. In the above example I'm moving apps that have Keep in Dock set and not set. They're all re-arrangeable.