I just finished a plugin for Sketch which allows you to save and load colors into the color picker. Check it out:
It grabs the colors from the Document Colors section of the color picker and saves them as a .sketchpalette file, which you can then share with other people that have the plugin. Loading the palette file replaces the colors in the Document Colors section of the color picker for the current document. There is also a command to just clear out all of the Document Colors.
Let me know what you think!