Symptoms
It is possible to configure the K2 for SharePoint 2013 app to work with a site in SharePoint that is configured with Forms Based Authentication.
Diagnoses
Currently, this item is not documented, however is still achievable.
Resolution
A script can be run against the default K2 Forms STS to configure it to look at the correct Issuer Thumbprint and update the ClaimTypeMap and ClaimTypeMapping tables with the proper information. At this point, a custom User manager will need to be configured so that all users signing in with Forms Auth from SharePoint could be verified against the correct user repository and cached against a new label in K2. This allows K2 to be able to find and authenticate users when receiving creds from SharePoint where users signed in using forms based authentication.
Please contact K2 Support for the proper configuration method, as this item is not found in existing documentation.