You can add the "Variable Editor (Formatter)" to the Story form, or any other task form, that is generated by a record producer. This KB article explains the process: Determining whether the Variable Editor is added to a form - Support and Troubleshooting
When you fill out the record producer form, it looks like a record is created on the sc_item_produced_record table that links the generated Story record to the variables/questions from the request form.
My desire is slightly different. I'd like to use a standard catalog item instead of a record producer. I want the flow that runs to be able to gather approvals or additional information before the Story task is created. I hoped I'd be able to fill in some reference field on the Story record that could link the story back to the variables from the catalog item. In the longer term, I'm interested in adding a new step type in the Step Based Request Fulfillment flow as described in the documentation. Maybe that custom step could create the story and link it to the variables? Create a service fulfillment step type
