Grammar in Google Web Speech API

Correct answer is: no, you can’t. =(

I can’t speak for Chrome, but in Android they are quite clear that you cannot provide a grammar. In Android speech recognition you are limited to a choice of two models: “free form” and “web search”.

See Android: Speech Recognition Append Dictionary?

For Google Cloud Speech API (Not Web Speech API) but some may find this useful:

Although currently in beta, Google has released new capability which allows you to

include a list of phrases to act as “hints” to Cloud Speech-to-Text. Providing these hints, a technique called speech adaptation, helps Speech-to-Text API to recognize the specified phrases from your audio data.”

See cloud.google.com/speech-to-text/docs/context-strength