How to have my admin start a template and then send into the flow

This is possible.  You should share the Template with the “admin” so they can use the Template, then also set the Template usage to either, ‘Quick send with advanced edit option’ or ‘Advanced edit only’. When the “admin” selects “Use” on the Template they enter in the appropriate Recipients then select Next or “Advanced Edit” depending on the Template Usage setting.  This would bring them to the DocuSign fields which they can pre-fill by selecting a field and typing in the “Add Text” box or double clicking the field and directly typing into the DocuSign field.  They fill out the necessary boxes and then hit Send.