I love these old vintage chests that show traces of former incarnations in their paint colors. You know at some point it had been solidly painted all of the colors above and probably more. Using Annie Sloan Chalk Paint in these colors and the tints shown below will create a similar finish.
Usually I layer the colors, purposely leaving gaps, to create a look of wear. Another technique I use is to dip one side of my brush in one color and the other side in a different color. Laying your paint on in this way results in areas where the colors are separate, but also where the paint mixes and becomes a third color, increasing depth and texture.
To match the colors on this piece you will have to play a bit combining Pure White, with the Greek Blue, the Henrietta, and the English Yellow in approximatly equal parts or 1:1. Being exact is not important, and you may end up with more or less white in your color combinations. If you don't have Pure White you can use Old White, although your tints will be slightly different. The character of a vintage piece is enhanced by these variations and imperfections. Part of its charm is knowing it was painted by hand.