Data flowing into and out of a system are usually called Context Diagrams. I can't see that this is very attractive to customers but they are very good specially in projects where data integration is considered and ETL/DW projects.
You could also use DFDs to show the same information, however, DFDs are not common. They were very popular with batch systems.
The questions here is what do you want to show? If you are showing a process flow then use BPMN or UML Activity Diagrams. If you are showing integration then Context Diagrams or DFDs will do. If you want to show a work flow, then a UML Activity Diagrams or BPMN. There are other tools for showing other aspects of requirements too.
What you want to make sure of is to get feedback and communicate with customer. Some customers want text, most love simple pictures. You challenge is to communicate accurate information although there is no perfect tool.