Currently, there's a pull request for emscripten to make the SDL implementation use the Web Audio API (it currently uses the Mozilla Audio API, which is why Chrome was silent): https://github.com/kripken/emscripten/pull/1299 In that same pull request, I believe there were many improvements made to the buffer streaming support.
Otherwise, the OpenAL implementation uses Web Audio and has buffer streaming support currently in the master branch.