Streaming data to an HTTP endpoint with Amazon Kinesis Data Firehose

There are some good tutorials that can help you understand how to configure API Gateway - https://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-rest-tutorials.html

Kinesis DF expects a specific response format - see https://docs.aws.amazon.com/firehose/latest/dev/httpdeliveryrequestresponse.html for details. The same responseId from the request sent to a HTTP destination must exist as well in the response. If you can not influence HTTP destination so it replies with the expected format you can use API Gateway Rest API with the integration type of HTTP. There you can define VTL templates to map responses from the target. The only way I know to remember requestId between the request and the response is to add an integration request template

#set($context.requestOverride.header.request-id = $util.parseJson($input.body).requestId)
$input.json('$')

and then in the integration response template:

#set($requestId = $context.requestOverride.header.request-id)
{
  "requestId": "$requestId",
  "timestamp": $context.requestTimeEpoch
}