Imported photo texture flashes as I orbit

I imported a .jpg file to form a texture to show on the inner face of an L-shaped component. In order to bend the image around the inside of the “L” I declared it “projected”, and I sampled and painted it onto the inside of the corner wall. I moved the component, now named “Folded on Left” into a scene showing the inside of a room, with a section cut to look at the interior corner. When I orbit the scene slowly, the image flashes in and out of visibility.
Here is a link to the public file in Dropbox: https://dl.dropboxusercontent.com/u/64862283/Furnished%20with%20chest%20vers%2021.skp; the scene in question is “Folded on Left”.

It’s called Z-Fighting and happens when two faces try to occupy the same space.
Move it away from the wall or give it some thickness, or project it onto the wall itself.

By the way, the gray faces are back faces, you should orientate everything so the white faces face out.