I'm not aware of any open web APIs available to Swift Kanban, otherwise I'd have attempted to create a solution for this myself.
I'd love to see an Outlook add-in to help with organizing, labeling and quickly finding email communications pertaining to archived and current Kanban cards/projects. The inbox view could allow you to "tag" or label existing email conversations simply by selecting the Kanban card number/project name from a drop down list within Outlook's Add-In or toolbar ribbon. Replies and response conversation threads for a previously labeled communications would need no further labeling. Also perhaps a setting that will add a reference "signature" at the end with the Kanban card number and a link to the card? Or perhaps a prompt when hitting send on a brand new email thread asking if the email being sent needs to be "tagged" with a Kanban project? Down the road perhaps this add-in could also feed email communication timestamps into the Kanban cards for card activity measurements.