There’s not a way to derive a VoD from the broadcast ID that I’m aware of, but as far as I’ve seen the broadcast ID is the same as the _id of a stream on /kraken/streams. There used to be a JTV API endpoint to query for a broadcast ID, but that’s long gone. Your best bet would be to grab /kraken/channels/:channel/videos?broadcasts=true for the channel, and match broadcast_id to the stream’s _id.