How to send Prometheus data to CloudWatch?

Not sure if this is what you are looking for , but you can use Amazon CloudWatch to monitor Prometheus metrics from Amazon Elastic Containers (ECS), Amazon Elastic Kubernetes Service (EKS), AWS Fargate, and Kubernetes clusters, now publicly available.

Some reference - Amazon CloudWatch Prometheus metrics now generally available

To add further to the answer by "AWS-User_Nitin"

....You can use Amazon CloudWatch to monitor Prometheus metrics from Amazon Elastic Kubernetes Service (EKS) and Kubernetes clusters. You can expose custom metrics on those services, and ingest the Prometheus metrics in CloudWatch. By curating the collection and aggregation of Prometheus metrics, CloudWatch users can monitor, troubleshoot, and alarm on application performance degradation and failures faster while reducing the number of monitoring tools required.

A guide is available [1] on how to setup the integration to monitor workloads which is a practical workshop. Additionally, if you run into any issues with metrics on CloudWatch side, then we have a troubleshooting guide [2] to assist narrowing down the issue with integration.

[1] https://aws.amazon.com/blogs/containers/using-prometheus-metrics-in-amazon-cloudwatch/

[2] https://docs.amazonaws.cn/en_us/AmazonCloudWatch/latest/monitoring/ContainerInsights-Prometheus-troubleshooting.html