Should we use flow charts, swim lanes, value stream mapping, proprietary software notation, or BPMN? Yes, there a number of notations you could use, and you want to pick the right one for your organization.
The first question to ask is what is the purpose of the process diagramming notation? Since there are several purposes for process diagramming at different stages of a BPM/ process improvement project, you may switch to one type of notation or another at different times.
Purpose 1: A high level map to scope the project and as part of the charter. Here I suggest using a simple flow chart with 6-10 steps using rectangle for activities/steps, diamond shaped decision diamonds and directional arrows. You could actually create it in PowerPoint, but I usually do it in Visio. The purpose of this map is to get people understanding what a process looks like.
A high level process map is: