Chrome Canary already has dawn 'built-in', you just need to enable it on the 'chrome://flags' page. The setting you need to enable is called 'Unsafe WebGPU
'.
Recent versions of emscripten have excellent built-in webgpu support, you just need to add '-sUSE_WEBGPU' to the em++ command line options when linking.The headers are <webgpu/webgpu.h> and <webgpu/webgpu_cpp.h>.
Good luck!
Mark