How to Create Live connection between Amazon Redshift and Amazon RDS (MySQL)
In order to create a live connection from MySQL to Redshift you need to choose an appropriate database replication method. Among all existing methods, the Change Data Capture (CDC) is the most suitable for your case. 

In this method, after a dump of the initial state of the database, the log of each database operation is continuously streamed and loaded into the data warehouse, and consolidated on a schedule (configurable) and the biggest advantage is that it enables near real-time replication.

A tool that I had a good experience with is Alooma, it can support near real time connection between Amazon Redshift and MySQL data base.