The Flow/Catalog process is designed for you to specify the flow you want from the catalog item itself, and you are correct that it will only trigger on item submission. Because of all of that the sc_req_item table is not selectable in the table picker in the trigger section.
However, you can still call a flow/subflow from a script using the FlowAPI. I know it's a bit of a workaround, but I would create a subflow where the input is a Request Item record:
Then you can call that from a business rule that runs on update via the flow API and pass the current object. I didn't actually test this so it's possible you may have to play around with passing the current object into the subflow, but I think this overall architecture may be your best way forward.
