First off, how would you architect this without Prefect? Would you use object storage (e.g., S3) or block storage (e.g., an EBS volume attached to an instance) for storing such data artifacts? I would claim that the first option is better, cheaper, more reliable, and even easier to set up.
That's why I would also not use any mounted volume for that in Prefect as it introduces a lot of (unnecessary?) complexity with no extra benefit.
Having said that, if you have some restrictions imposed upon you from above (aka someone told you to use a mounted volume for storing run artifacts regardless of whether this is a good idea), check out this thread:
https://discourse.prefect.io/t/how-to-mount-a-folder-on-my-local-filesystem-to-a-flow-run-pod-on-kubernetes/441