Cash flow per share is simply cash flow divided by the number of shares in issue.
As there are many different cash flow measures, calculating a cash flow per share requires choosing one. It would be logical to use a measure of cash flow after interest as this is a per share measure and therefore want something related to returns to shareholders.
Free cash flow after interest would be a good choice that meets the above requirements, but it is not the only possible choice.
The most common reason for calculating cash flow per share is to calculate price/cash flow