You’ll first need to draft your network setup as is on OVH, then design the same on AWS, first address custom overlay networks if any. Answer questions like these in your design:
Do you have overlay networks? If yes, which driver does it use?, can you redo the same on AWS?
How’s the container inter-linking done is it shared file systems/volumes, or monitoring network/containers, or any association with physical host servers?
If there is shared storage on OVH that means you have data migration considerations to address before migrating.
This planning will make migration simpler. You can migrate to Rancher on AWS, then switch to k8s with ease.
Rancher makes it easy to configure, deploy and manage Kubernetes, on any infrastructure. This is an explanation: https://rancher.com/kubernetes/.
And if your container runtime is purely docker, you can easily move the setup to AWS. Application setup is the main contributor to any complexities.