I did a quick test, and on my machine the Sky Atmosphere is working on Desktop Forward shading (DX11 and DX12). Tested on the sample FPS demo.
Double checked in the documentation (article: Supported Features by Rendering Path: Desktop and Desktop XR) :
Maybe the issue come from somewhere else, and you can probably use forward rendering on Desktop for your project, for better performance. Be careful though with dynamic lights as they have a certain cost on a forward renderer (bigger than in deferred rendering)