When VisualStudio code was announced I went out and installed it right away on my Mac and Windows machines. One my home development machine I was unable to see the icons. I was thinking that it was due to my 4K display and an High DPI issue but it turns out not to be the case.
In reading the Reacting to feedback, common issues, and our first update post on the Visual Studio Code bug it was due to the svg file extension being associated to something other than image/svg+xml in my case due to Inkscape it was set to application/svg.
Changing the Content Type to image/svg+xml made the icons visible.
There is a FAQ with several fixes and workarounds for Visual Studio Code at https://code.visualstudio.com/Docs/FAQ