How can I find out the storage usage of a Redshift cluster?

This metric is not directly available but can be calculated using Cloudwatch get-metric-statistics and Redshift describe-clusters

aws cloudwatch get-metric-statistics --region <your-cluster-region> --metric-name PercentageDiskSpaceUsed --namespace AWS/Redshift --statistics Maximum --dimensions="Name=ClusterIdentifier,Value=<your-cluster-identifier>" --start-time <yyyy-mm-ddThh:mi:ss> --end-time <yyyy-mm-ddThh:mi:ss> --period 3600

This will give you PercentageDiskSpaceUsed in Percentage example 2.098025

aws redshift describe-clusters --cluster-identifier <your-cluster-identifier> --region <your-cluster-region>

This will give you TotalStorageCapacityInMegaBytes example 4000000

From these two values you will calculate 2.098025 percent of 4000000 to get storage usage in MB between the start time and end time. This should be a good estimate of the backup size for that cluster.