Customers can now configure Amazon API Gateway to send API access logs to Amazon Kinesis Data Firehose. It’s easy to configure Kinesis Data Firehose as a log destination by enabling access logging on an API and specifying the Firehose stream. 

from Recent Announcements https://aws.amazon.com/about-aws/whats-new/2019/10/amazon-api-gateway-now-supports-access-logging-to-amazon-kinesis-data-firehose/