Chrome OS started syncing Wallpapers long back. The next step forward, syncing our custom wallpapers, is coming (most probably) in the next Dev channel update.
Here is the commit log:
Add auto sync custom wallpaper support
Sync wallpaper in storage onchange events, will also upload wallpapers to server when user set custom wallpaper
So, how does it work? .When you set a custom wallpaper, Google will upload it to the sync server in the background, and make it available on any other Chrome OS device that you use. It may take a while depending on your connection speed.
Wait for this feature in one of the upcoming Chrome OS releases!