@Bay Leaf Digital , I'm a little late to seeing your question, but you have two options for achieving this.
One, you can set up an endpoint (or use some other means) that would allow you to issue an event to the hosting page that includes the JSON data. When the page receives the event you use Web Chat's store to dispatch a message to Web Chat that includes the data. There is a sample, located here, that details the opposite of this (Web Chat activity spawns event on the page). It's the same concept except that you are reversing the process.
Two, you can set up an endpoint in your bot to be used for receiving proactive messages. In this scenario, you send a POST request to the endpoint which then allows the bot to ingest the incoming data. In doing so, it becomes part of the conversation and then would be displayed via Web Chat.
Both options are relatively simple to set up, though the second entails less to do, overall. You just need to decide which method you favor.