With Kanban you don't really have the problem of the sprint ending before you are happy that a feature is fully tested and working, so there is no need for an equivalent hardening sprint. Instead you would hold the work item in the test state until you have a robust set of automated test that verify the acceptance criteria. Limiting the work in progress means that is there are a lot of testing tasks then the team will need to focus on reducing this before new work items can begin.
Performance and Load testing should be ongoing and part of the test state and added to for each work item that enters into this state if required.
As for exploratory testing, you can arrange a time, for example every Monday 9am to 11am , that the whole team will do exploratory testing and then discuss the results.
You will also need a mechanism for keeping incomplete features out of a deployed build such as feature switch that will allow you to turn on and off a particular feature.