I did a Tesla turbine principle based automotive turbine design as a senior year engineering design project many decades ago; and, based upon the gas flow study in that project, there is a flow dynamics principal that I anticipate will be a problem in applying the Tesla disc in your device.
One of the basic fluid flow principles taken advantage of in Tesla's edge tangent inflow and center exhaust design is what is known in Computational Flow Analysis as the natural source - sink vortex flow pattern of fluid dynamic that drives a radial vortex flow from the disc edge to its center. This natural flow tendency is one factor that gives the Tesla turbine its high efficiency. (PS Tesla's genius went far beyond electricity and I am convinced he was well aware of how this flow principal would contribute to his design.)
What you are trying to do is draw air into the edge of the disc set for a partial rotation and then eject it from that edge at a separate bottom tangent point where the two discs diverge. Due to the natural fluid vortex tendency, the air is actually going to try to continue its vortex flow around the discs (assisted by the friction of the discs as well) to the point where the top where discs converge; and, thereby create a high pressure region at that top point that will counteract the inflow of additional external incoming air from that region and potentially make your device a very inefficient lift generator.