Here is the picture I chose:
I clicked my "Chip It" button which put it on the screen, then clicked it again and it came up with colors.
If you don't like the colors it comes up with (I didn't like that it didn't include the green), you can select 'More Colors' at the bottom and it will expand to include all like it did above.
Go to a Flickr picture you like. I used Paint to pull a print screen image from my own Flickr account to show you how it will work.
Say this is the image I want to "chip". You are supposed to run the mouse over the picture but it doesn't work on the larger image. It does, however, work on the small images in your photostream over on the right.
So find your image in the center there and roll over it. Then click "chip".