I have a k8s cluster deployed in AWS's EKS and I want to change horizontal-pod-autoscaler-sync-period from the default 30s value.
How can I change this flag?
Unfortunately you are not able do this on GKE, EKS and other managed clusters.
In order to change/add flags in kube-controller-manager - you should have access to your /etc/kubernetes/manifests/ dir on master node and be able to modify parameters in /etc/kubernetes/manifests/kube-controller-manager.yaml.
GKE, EKS and similar clusters manages only by their providers without getting you permissions to have access to master nodes.
Similar questions:
1) horizontal-autoscaler-in-a-gke-cluster
2) change-the-horizontal-pod-autoscaler-sync-period-with-gke
As a workaround you can create cluster using kubeadm init and configure/change it in any way you want.