You can use one of several available methods for remapping. Unfortunately, there is no hardware button on the type cover or on the Surface Pro itself that would result in a middle click out of the box, so you are going to have to sacrifice some other key or key sequence to get middle click.
For example, with AutoHotkey, you can "remap" a simultaneous left and right click (this may actually be hard to pull off with the Type Cover touchpad; I have one, and it's hard enough to click a single button!) to a middle click. Or, you could remap something like Ctrl+Left-Click to a middle click.
The AutoHotkey Documentation contains more information how to do this using various methods, including a "pure" Windows Registry edit that has nothing to do with AHK and appears to work better in some situations / for some programs. So you'll basically have to try a bunch of different ways and key combinations until you find one you can live with.
Or get an external USB or bluetooth mouse that has a middle mouse button or the ability to "click" the scroll wheel, and forget about the type cover's touchpad...