When working with multiple 3D Warps layers, remember that even though the objects are in the same 3D space, they still react to the After Effects layer hierarchy. This means, if layer A is on top of layer B, the page for layer A will be on top of layer B even if the page for layer B is sitting on top (position wise).
To get the page flip effect to work correctly, the page that is flipping will always need to be the top layer. After it completes the flip, duplicate the layer, and place it below the new page that is flipping. This way, as the new page is flipping, it will show up above the page that had completed the page flip. You will also need to adjust the length of the layers for this to work properly.
It may be tricky to set up the first page flip. However, once you do one, the process will be the same for the rest of the page flips.