I've worked with some customers doing that already, in Oracle. Seems also that LinkedIn uses a lot that technique of streaming data from databases to somewhere else. They created a platform called Databus to accomplish that in an agnostic way - https://github.com/linkedin/databus/wiki/Databus-for-MySQL.
There is a public project in Github, following LinkedIn principles that is already streaming binlog from Mysql to Kinesis Streams - https://github.com/cmerrick/plainview
If you want to get into the nitty gritty details of LinkedIn approach, there is a really nice (and extensive) blog post available - https://engineering.linkedin.com/distributed-systems/log-what-every-software-engineer-should-know-about-real-time-datas-unifying.
Last but not least, Yelp is doing that as well, but with Kafka - https://engineeringblog.yelp.com/2016/08/streaming-mysql-tables-in-real-time-to-kafka.html
Not getting into the basics of Kinesis Streams, for the sake of brevity, if we bring Kinesis Streams to the game, I don't see why it shouldn't work. As a matter of fact, it was built for that - your database transaction log is a stream of events. Borrowing an excerpt from Amazon Web Services public documentation: Amazon Kinesis Streams allows for real-time data processing. With Amazon Kinesis Streams, you can continuously collect data as it is generated and promptly react to critical information about your business and operations.
Hope this helps.