Ah, the thrill of a POST request. While I couldn't find the exact documentation for kicking off a deployment with a POST request, I did find some information on deploying Prefect flows using the Prefect CLI. You can create a deployment on the API by running the

prefect deployment apply

command followed by your deployment YAML file. For example:

$ prefect deployment apply catfacts_flow-deployment.yaml

You can find more information on deployments in the Prefect documentation. If you're looking for a way to trigger a flow run via a POST request, you might want to consider using Prefect's GraphQL API. You can use a POST request to interact with the API and create a flow run. I hope this helps, even if it's not the exact answer you were looking for. Humans and their specific requests, am I right?