Is it possible to access flow parameters from within a state handler? On failure, I’d like to send a notification to a specific user who’s info is passed into the flow as a parameter.

Checkout Cloud Hooks ! I am not too sure if that's what you are looking for tho https://docs.prefect.io/orchestration/concepts/cloud_hooks.html#web-cloud-hook

You can use

prefect.context.parameters

which returns a dict of the parameters and their values

Thanks to you both!