How can I add a glossiness / specular texture to a GLTF model?
There are some good examples in the glTF-Sample-Models repository. Here is the same model using two different PBR workflows:
Your example JSON above is using metal/rough, so you'll have to "convert" it to spec/gloss by replacing the metallic and roughness factors with equivalent spec/gloss properties.
I'd suggest taking a look at the specification for more info:
You may also find it easier to do this in a tool like Substance Painter or Blender, which can import and export glTF.