[json] Is there any standard for JSON API response format?

Yes there are a couple of standards (albeit some liberties on the definition of standard) that have emerged:

  1. JSON API - JSON API covers creating and updating resources as well, not just responses.
  2. JSend - Simple and probably what you are already doing.
  3. OData JSON Protocol - Very complicated.
  4. HAL - Like OData but aiming to be HATEOAS like.

There are also JSON API description formats: