In Jira natively there is not an option to display this on the board directly, however you could create a dashboard and use the JIRA Charting Plugin as described in the following KB to generate a Average time in Status Gadget to track this data, but this is going to be on a separate dashboard not the Card directly:
Alternatively, I believe you could use ScriptRunner's scripted fields to create a field similar to their "Total time this issue has been In Progress" field, and modify for changes between each status rather than created to current as it is currently written.
I have multiple projects that use variations of the same base workflow. The variations depend on the requirements of the project or issue type. The variations mostly come in the form of new statuses ...
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