Symptoms

You may face some errors when installing K2 for SharePoint application due to absent/disabled/misconfigured SharePoint 2013 Distributed Cache Service Instance. You may get some errors upon adding K2 for SharePoint app and some errors in SharePoint logs related to this.
 

Diagnoses

Whereas K2 for SharePoint does not rely directly on Distributed Cache Service when not installed, disabled or misconfigured, this service may cause issues/problems with K2 for SharePoint application and SharePoint environments in general. Microsoft does not state that this service is required for certain features apart from mentioning what is being cached and which SP features can leverage/rely this cache. Misconfigured or not installed Distributed Cache Service may cause issues with SharePoint 2013 environments, especially for SharePoint farms with more than one WFE server.
Distributed Cache caches the calls that should go to the WFE servers, and it is especially important for SharePoint farms where request could be send to the next WFE server, on which local cache is not the same as on WFE server where the call originated (e.g. Round Robin scenario).
When processing requests, especially something like OAuth which is dependent on User Profile data, SharePoint first tries to pull it from the local web cache. If it cannot found anything there, it next attempt to get necessary information from the Distributed Cache. If Distributed Cache does not have required information (or disabled) then SharePoint has to try and resolve request without cache, and this could lead to timeouts, and other issues such as the Search Service that would not work under specific requirements or the User Profile Connections that does not return in time.
 

Resolution

Based on aforementioned information Distributed Cache should be installed and properly configured for SharePoint 2013 farms with more than one WFE servers.
This issue is a problem with SharePoint farm configuration, which should be configured properly before being used with K2.
For single server environments absent or disabled Distributed Cache Service should not have any negative impact or cause issues with K2 for SharePoint application.