Flink would potentially replace the processing that's done in Redshift.
Instead of Kinesis -> Redshift with processing as part of the load (ETL) or after the load (ELT), you would read from Kinesis into Flink, transform your data, and then write it to Redshift.
Flink provides the potential advantage of lower latencies in your data processing as you can process your data as a stream, not batched.
Performance is extremely subjective - it depends where your current bottlenecks are. Depending on your data patterns though, processing it as a stream can help with performance as you smooth out the consumption and processing instead of it all bunching up and needing processing at once (i.e. batch).