I am adding the flag --cloud-provider=aws to /etc/kubernetes/manifests/kube-apiserver.yaml and kube-controller-manager.yaml. When I describe the pods I can see that they pick up the change and are recreated, however the flags have not changed.
Running on Centos7 machines in AWS. I have tried restarting the Kubelet service and tried using kubectl apply.
There are couple of ways to achieve this. But seems like you have choosen the DynamicKubeletConfig way but you didn't configure DynamicKubeletConfig! To do live changes to your cluster you need to enable DynamicKubeletonfig first then follow the steps here
Another Way [Ref]
TL;DR (do this at your own risk!)
Step 1: kubeadm config view > kubeadm-config.yaml
Step 2: edit kubeadm-config.yaml to add your changes [Reference for flags ]
Step 3: kubeadm upgrade apply --config kubeadm-config.yaml