Normal user Flipnote publication happens through Flipnote Studio. After connecting to RexiMemo and signing in, open a channel in the DSi service and use the in-app posting flow to select and publish the Flipnote.
The website and personal API do not provide a general endpoint for publishing an arbitrary uploaded PPM. The verified S2R migration workflow is a separate import process for moving eligible Sudomemo Flipnotes, and administrators have separate moderation/import tools.