I am attempting to describe in a cloudformation template, a HTTP listening API gateway to post any incoming json requests through to a Kinesis data stream, with the intention of batch processing later.

When the API Gateway has a protocol of HTTP however, the integration type can only be one of AWS\_PROXY, or HTTP\_PROXY.

When I use AWS\_PROXY, then I receive the message that I can only stream to either Lambda, or Firehose. 

Am I missing something? Can I not put the incoming messages directly onto a Kinesis datastream?

Thanks.