Integrating MongoDB and Amazon Kinesis can help build intelligent, durable streams for real-time data processing. By using MongoDB Stitch Triggers, developers can automatically send updates to a Kinesis stream when relevant data changes in their MongoDB database. This setup allows for efficient streaming analytics on data such as cart abandonment or credit card fraud detection. The integration involves creating a Stitch application, configuring services to interact with external services like AWS Kinesis, writing functions to put records into the stream, and setting up triggers that watch specific operations in the MongoDB database. Once the data is in the Kinesis stream, additional services can be used downstream for analytics or processing, such as Amazon Kinesis Data Analytics.