The shaders themselves are authored using BGFX's own shader language, which broadly mimics GLSL but has some caveats.
The relevant JSON files have comprehensive inline documentation inline in the form of comments in certain ones:
Chains: bgfx/chains/hlsl.json
Effects: bgfx/effects/misc/blit.json
That should pretty much cover everything, but if you have any specific questions, feel free to ask.