Thanks to the advice I got here I ended up painting my skin gray with watercolors (gesso as a base with a little bit of lamp black watercolor). It was great! Once it was dry it didn't wipe off too much, and it was easy to take off with soap and water.
I made the dress, the shrug, the purse, and the gloves. I also painted the fan and dyed the stockings.
And here I am compared to Louise Brooks
I didn't attempt to be 1920s historically accurate because I only had one week to make the costume, but the feel is similar.
There are a ton more pictures on my flickr