By adopting a methodology like Kaban, your team will be working in a living backlog (that can change at any moment) and they will limit work in progress according to their capacity. Kaban is about continuous delivery, so there will be a release every time the team is ready to do it.
Testing is always taking place and is essential to consider the story ready for delivery.
ou may have a look at the previous instructions for Scrum teams as most of it can also be applied to Kanban teams.
In Kanban, you're limiting the amount of WIP issues in a given state, namely, the ones that are in testing. Because you're not dividing your release into several periods of time, as you do with Scrum, you can manage it as if the period would embrace the time frame of the release.
Thus, you can have a Test Plan to track the Tests related to the features being addressed on the Kanban board. You may complement it with additional Test Plans, namely, for tracking the regression testing. It may be a good approach to have the Test Plan with regression tests, or smoke tests, as an independent Test Plan, so it is more apparent if regression is occurring or not.